Abstract As a crucial medium of information dissemination, text holds a pivotal role in a multitude of applications. However, text detection in complex and unstructured environments presents significant challenges, such as the presence of cluttered backgrounds, variations in appearance, and uneven lighting conditions. To address this issue, this study proposes a text detection framework that leverages multistage edge detection and contextual information. This framework deviates from traditional approaches by incorporating four primary processing steps, including text visual saliency region detection to accentuate the text regions and diminish background interference, multistage edge detection to enhance the conventional stroke width transform results, a texture-based and connected components-based integration to accurately distinguish text from the background, and a context fusion step to recover missing text regions and improve the recall of text detection. The proposed method was evaluated on two widely used benchmark datasets, i.e., the international conference on document analysis and recognition (ICDAR) 2005 dataset and the ICDAR 2011 dataset, and the results indicate the advancedness of the method.
{"title":"Feature fusion-based text information mining method for natural scenes","authors":"Feng Peng, Runmin Wang, Yiyun Hu, Guang Yang, Ying Zhou","doi":"10.1515/dema-2022-0255","DOIUrl":"https://doi.org/10.1515/dema-2022-0255","url":null,"abstract":"Abstract As a crucial medium of information dissemination, text holds a pivotal role in a multitude of applications. However, text detection in complex and unstructured environments presents significant challenges, such as the presence of cluttered backgrounds, variations in appearance, and uneven lighting conditions. To address this issue, this study proposes a text detection framework that leverages multistage edge detection and contextual information. This framework deviates from traditional approaches by incorporating four primary processing steps, including text visual saliency region detection to accentuate the text regions and diminish background interference, multistage edge detection to enhance the conventional stroke width transform results, a texture-based and connected components-based integration to accurately distinguish text from the background, and a context fusion step to recover missing text regions and improve the recall of text detection. The proposed method was evaluated on two widely used benchmark datasets, i.e., the international conference on document analysis and recognition (ICDAR) 2005 dataset and the ICDAR 2011 dataset, and the results indicate the advancedness of the method.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43807416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In the current manuscript, we combine the q-fractional integral operator and q-fractional derivative to investigate a coupled hybrid fractional q-differential systems with sequential fractional q-derivatives. The existence and uniqueness of solutions for the proposed system are established by means of Leray-Schauder’s alternative and the Banach contraction principle. Furthermore, the Ulam-Hyers and Ulam-Hyers-Rassias stability results are discussed. Finally, two illustrative examples are given to highlight the theoretical findings.
{"title":"Application of fractional quantum calculus on coupled hybrid differential systems within the sequential Caputo fractional q-derivatives","authors":"J. Alzabut, M. Houas, M. Abbas","doi":"10.1515/dema-2022-0205","DOIUrl":"https://doi.org/10.1515/dema-2022-0205","url":null,"abstract":"Abstract In the current manuscript, we combine the q-fractional integral operator and q-fractional derivative to investigate a coupled hybrid fractional q-differential systems with sequential fractional q-derivatives. The existence and uniqueness of solutions for the proposed system are established by means of Leray-Schauder’s alternative and the Banach contraction principle. Furthermore, the Ulam-Hyers and Ulam-Hyers-Rassias stability results are discussed. Finally, two illustrative examples are given to highlight the theoretical findings.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44445772","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this article, we present a structure result concerning fuzzy fractals generated by an orbital fuzzy iterated function system ( ( X , d ) , ( f i ) i ∈ I , ( ρ i ) i ∈ I ) left(left(X,d),{({f}_{i})}_{iin I},{left({rho }_{i})}_{iin I}) . Our result involves the following two main ingredients: (a) the fuzzy fractal associated with the canonical iterated fuzzy function system ( ( I N , d Λ ) , ( τ i ) i ∈ I , ( ρ i ) i ∈ I ) left(left({I}^{{mathbb{N}}},{d}_{Lambda }),{left({tau }_{i})}_{iin I},{left({rho }_{i})}_{iin I}) , where d Λ {d}_{Lambda } is Baire’s metric on the code space I N {I}^{{mathbb{N}}} and τ i : I N → I N {tau }_{i}:{I}^{{mathbb{N}}}to {I}^{{mathbb{N}}} is given by τ i ( ( ω 1 , ω 2 , … ) ) ≔ ( i , ω 1 , ω 2 , … ) {tau }_{i}left(left({omega }_{1},{omega }_{2},ldots )):= left(i,{omega }_{1},{omega }_{2},ldots ) for every ( ω 1 , ω 2 , … ) ∈ I N left({omega }_{1},{omega }_{2},ldots )in {I}^{{mathbb{N}}} and every i ∈ I iin I ; (b) the canonical projections of certain iterated function systems associated with the fuzzy fractal under consideration.
摘要本文给出了一个关于轨道模糊迭代函数系统（（X，d），（f i）i∈i，（ρi）i≠i）left（left（X，d）{({f}_{i} ）｝_｛i in i｝，｛left（｛rho｝_{i｝）｝。我们的结果涉及以下两个主要成分：（a）与正则迭代模糊函数系统（（I N，d∧），（τI）I∈I，（ρI）I≠I）left（left（｛I｝^｛mathbb｛N｝｝）相关的模糊分形，{d}_｛Lambda｝），｛left（｛tau｝_｛i｝{d}_｛Lambda｝是码空间I N｛I｝^｛｛mathbb｛N｝｝和τI:I N上的Baire度量→ I N｛tau｝_｛I｝：｛I｝^｛mathbb｛N｝｝ to｛I’^｛ mathbb｝｝∈I Nleft（｛omega｝_｛1｝，｛omega｝_｛2｝，ldots）在｛I｝^｛mathbb｛N｝｝｝｝中，并且I中的每个I∈I I；（b） 与所考虑的模糊分形相关的某些迭代函数系统的正则投影。
{"title":"The structure of fuzzy fractals generated by an orbital fuzzy iterated function system","authors":"Irina Savu, Radu Miculescu, Alexandru Mihail","doi":"10.1515/dema-2022-0217","DOIUrl":"https://doi.org/10.1515/dema-2022-0217","url":null,"abstract":"Abstract In this article, we present a structure result concerning fuzzy fractals generated by an orbital fuzzy iterated function system ( ( X , d ) , ( f i ) i ∈ I , ( ρ i ) i ∈ I ) left(left(X,d),{({f}_{i})}_{iin I},{left({rho }_{i})}_{iin I}) . Our result involves the following two main ingredients: (a) the fuzzy fractal associated with the canonical iterated fuzzy function system ( ( I N , d Λ ) , ( τ i ) i ∈ I , ( ρ i ) i ∈ I ) left(left({I}^{{mathbb{N}}},{d}_{Lambda }),{left({tau }_{i})}_{iin I},{left({rho }_{i})}_{iin I}) , where d Λ {d}_{Lambda } is Baire’s metric on the code space I N {I}^{{mathbb{N}}} and τ i : I N → I N {tau }_{i}:{I}^{{mathbb{N}}}to {I}^{{mathbb{N}}} is given by τ i ( ( ω 1 , ω 2 , … ) ) ≔ ( i , ω 1 , ω 2 , … ) {tau }_{i}left(left({omega }_{1},{omega }_{2},ldots )):= left(i,{omega }_{1},{omega }_{2},ldots ) for every ( ω 1 , ω 2 , … ) ∈ I N left({omega }_{1},{omega }_{2},ldots )in {I}^{{mathbb{N}}} and every i ∈ I iin I ; (b) the canonical projections of certain iterated function systems associated with the fuzzy fractal under consideration.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47926956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The main objective of this study is to define a new class of bipolar soft (BS) separation axioms known as BS T ˜ ˜ i {widetilde{widetilde{T}}}_{i} -space ( i = 0 , 1 , 2 , 3 , 4 ) left(i=0,1,2,3,4) . This type is defined in terms of ordinary points. We prove that BS T ˜ ˜ i {widetilde{widetilde{T}}}_{i} -space implies BS T ˜ ˜ i − 1 {widetilde{widetilde{T}}}_{i-1} -space for i = 1 , 2 i=1,2 ; however, the opposite is incorrect, as demonstrated by an example. For i = 0 , 1 , 2 , 3 , 4 i=0,1,2,3,4 , we investigate that every BS T ˜ ˜ i {widetilde{widetilde{T}}}_{i} -space is soft T ˜ i {widetilde{T}}_{i} -space; and we set up a condition in which the reverse is true. Moreover, we point out that a BS subspace of a BS T ˜ ˜ i {widetilde{widetilde{T}}}_{i} -space is a BS T ˜ ˜ i {widetilde{widetilde{T}}}_{i} -space for i = 0 , 1 , 2 , 3 i=0,1,2,3 .
{"title":"A novel class of bipolar soft separation axioms concerning crisp points","authors":"Baravan A. Asaad, Sagvan Y. Musa","doi":"10.1515/dema-2022-0189","DOIUrl":"https://doi.org/10.1515/dema-2022-0189","url":null,"abstract":"Abstract The main objective of this study is to define a new class of bipolar soft (BS) separation axioms known as BS T ˜ ˜ i {widetilde{widetilde{T}}}_{i} -space ( i = 0 , 1 , 2 , 3 , 4 ) left(i=0,1,2,3,4) . This type is defined in terms of ordinary points. We prove that BS T ˜ ˜ i {widetilde{widetilde{T}}}_{i} -space implies BS T ˜ ˜ i − 1 {widetilde{widetilde{T}}}_{i-1} -space for i = 1 , 2 i=1,2 ; however, the opposite is incorrect, as demonstrated by an example. For i = 0 , 1 , 2 , 3 , 4 i=0,1,2,3,4 , we investigate that every BS T ˜ ˜ i {widetilde{widetilde{T}}}_{i} -space is soft T ˜ i {widetilde{T}}_{i} -space; and we set up a condition in which the reverse is true. Moreover, we point out that a BS subspace of a BS T ˜ ˜ i {widetilde{widetilde{T}}}_{i} -space is a BS T ˜ ˜ i {widetilde{widetilde{T}}}_{i} -space for i = 0 , 1 , 2 , 3 i=0,1,2,3 .","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42286414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this article, we considered the pseudo-parabolic equation with Caputo-Fabrizio fractional derivative. This equation has many applications in different fields, such as science, technology, and so on. In this article, we gave the formula of mild solution, which is represented in the form of Fourier series by some operators . In the linear case, we investigated the continuity of the mild solution with respect to the fractional order. For the nonlinear case, we investigated the existence and uniqueness of a global solution. The main proof technique is based on the Banach fixed point theorem combined with some Sobolev embeddings. For more detailed, we obtained two other interesting results: the continuity of mild solution with respect to the derivative order and the convergence of solution as the coefficient k approaches to zero.
{"title":"On Cauchy problem for pseudo-parabolic equation with Caputo-Fabrizio operator","authors":"B. Nghia, V. T. Nguyen, L. Long","doi":"10.1515/dema-2022-0180","DOIUrl":"https://doi.org/10.1515/dema-2022-0180","url":null,"abstract":"Abstract In this article, we considered the pseudo-parabolic equation with Caputo-Fabrizio fractional derivative. This equation has many applications in different fields, such as science, technology, and so on. In this article, we gave the formula of mild solution, which is represented in the form of Fourier series by some operators . In the linear case, we investigated the continuity of the mild solution with respect to the fractional order. For the nonlinear case, we investigated the existence and uniqueness of a global solution. The main proof technique is based on the Banach fixed point theorem combined with some Sobolev embeddings. For more detailed, we obtained two other interesting results: the continuity of mild solution with respect to the derivative order and the convergence of solution as the coefficient k approaches to zero.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48507994","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this article, the stochastic fractional Davey-Stewartson equations (SFDSEs) that result from multiplicative Brownian motion in the Stratonovich sense are discussed. We use two different approaches, namely the Riccati-Bernoulli sub-ordinary differential equations and sine-cosine methods, to obtain novel elliptic, hyperbolic, trigonometric, and rational stochastic solutions. Due to the significance of the Davey-Stewartson equations in the theory of turbulence for plasma waves, the discovered solutions are useful in explaining a number of fascinating physical phenomena. Moreover, we illustrate how the fractional derivative and Brownian motion affect the exact solutions of the SFDSEs using MATLAB tools to plot our solutions and display a number of three-dimensional graphs. We demonstrate how the multiplicative Brownian motion stabilizes the SFDSE solutions at around zero.
{"title":"Impacts of Brownian motion and fractional derivative on the solutions of the stochastic fractional Davey-Stewartson equations","authors":"W. Mohammed, F. M. Al-Askar, M. El-Morshedy","doi":"10.1515/dema-2022-0233","DOIUrl":"https://doi.org/10.1515/dema-2022-0233","url":null,"abstract":"Abstract In this article, the stochastic fractional Davey-Stewartson equations (SFDSEs) that result from multiplicative Brownian motion in the Stratonovich sense are discussed. We use two different approaches, namely the Riccati-Bernoulli sub-ordinary differential equations and sine-cosine methods, to obtain novel elliptic, hyperbolic, trigonometric, and rational stochastic solutions. Due to the significance of the Davey-Stewartson equations in the theory of turbulence for plasma waves, the discovered solutions are useful in explaining a number of fascinating physical phenomena. Moreover, we illustrate how the fractional derivative and Brownian motion affect the exact solutions of the SFDSEs using MATLAB tools to plot our solutions and display a number of three-dimensional graphs. We demonstrate how the multiplicative Brownian motion stabilizes the SFDSE solutions at around zero.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49300507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract First, we introduce the concepts of equicontinuity, expansivity , ergodic shadowing property, and chain transitivity in uniform space. Second, we study the dynamical properties of equicontinuity, expansivity , ergodic shadowing property, and chain transitivity in the hyperspace of uniform space. Let (X,μ) left(X,mu ) be a uniform space, (C(X),Cμ) left(Cleft(X),{C}^{mu }) be a hyperspace of (X,μ) left(X,mu ) , and f:X→X f:Xto X be uniformly continuous. By using the relationship between original space and hyperspace, we obtain the following results: (a) the map f f is equicontinous if and only if the induced map Cf {C}^{f} is equicontinous; (b) if the induced map Cf {C}^{f} is expansive, then the map f f is expansive; (c) if the induced map Cf {C}^{f} has ergodic shadowing property, then the map f f has ergodic shadowing property; (d) if the induced map Cf {C}^{f} is chain transitive, then the map f f is chain transitive. In addition, we also study the topological conjugate invariance of (G,h) left(G,h) -shadowing property in metric G
首先，我们引入了均匀空间中的等连续性、扩张性、遍历阴影性和链传递性等概念。其次，研究了一致空间的超空间的等连续性、扩张性、遍历阴影性和链传递性的动力学性质。设(X， μ) left (X, mu)是一致空间，(C (X)，C μ) left (C left (X)，{C}^ {mu)是(X， μ)}left (X, mu)的超空间，f:X→X f:X to X是一致连续的。利用原始空间与超空间的关系，我们得到了以下结果:(a)映射f f是等连续的当且仅当诱导映射C f {C}^{f}是等连续的;(b)若诱导映射C f {C}^{f}是可扩张的，则映射f f是可扩张的;(c)若诱导映射c f {c} ^{f}具有遍历阴影性质，则映射f f具有遍历阴影性质;(d)如果诱导映射C f {C}^{f}是链传递的，则映射f f是链传递的。此外，我们还研究了(G,h) left (G,h)在测度G -空间中的拓扑共轭不变性，并证明了映射S S具有(G,h) left (G,h)阴影性当且仅当映射T T具有(G,h) left (G,h)阴影性。这些结果推广了超空间中的等连续性、扩张性、遍历阴影性和链传递性等结论。
{"title":"Dynamical property of hyperspace on uniform space","authors":"Zhanjiang Ji","doi":"10.1515/dema-2023-0264","DOIUrl":"https://doi.org/10.1515/dema-2023-0264","url":null,"abstract":"Abstract First, we introduce the concepts of equicontinuity, expansivity , ergodic shadowing property, and chain transitivity in uniform space. Second, we study the dynamical properties of equicontinuity, expansivity , ergodic shadowing property, and chain transitivity in the hyperspace of uniform space. Let <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>X</m:mi> <m:mo>,</m:mo> <m:mi>μ</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> left(X,mu ) be a uniform space, <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>C</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>X</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>,</m:mo> <m:msup> <m:mrow> <m:mi>C</m:mi> </m:mrow> <m:mrow> <m:mi>μ</m:mi> </m:mrow> </m:msup> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> left(Cleft(X),{C}^{mu }) be a hyperspace of <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>X</m:mi> <m:mo>,</m:mo> <m:mi>μ</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> left(X,mu ) , and <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>f</m:mi> <m:mo>:</m:mo> <m:mi>X</m:mi> <m:mo>→</m:mo> <m:mi>X</m:mi> </m:math> f:Xto X be uniformly continuous. By using the relationship between original space and hyperspace, we obtain the following results: (a) the map <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>f</m:mi> </m:math> f is equicontinous if and only if the induced map <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mrow> <m:mi>C</m:mi> </m:mrow> <m:mrow> <m:mi>f</m:mi> </m:mrow> </m:msup> </m:math> {C}^{f} is equicontinous; (b) if the induced map <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mrow> <m:mi>C</m:mi> </m:mrow> <m:mrow> <m:mi>f</m:mi> </m:mrow> </m:msup> </m:math> {C}^{f} is expansive, then the map <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>f</m:mi> </m:math> f is expansive; (c) if the induced map <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mrow> <m:mi>C</m:mi> </m:mrow> <m:mrow> <m:mi>f</m:mi> </m:mrow> </m:msup> </m:math> {C}^{f} has ergodic shadowing property, then the map <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>f</m:mi> </m:math> f has ergodic shadowing property; (d) if the induced map <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mrow> <m:mi>C</m:mi> </m:mrow> <m:mrow> <m:mi>f</m:mi> </m:mrow> </m:msup> </m:math> {C}^{f} is chain transitive, then the map <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>f</m:mi> </m:math> f is chain transitive. In addition, we also study the topological conjugate invariance of <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>G</m:mi> <m:mo>,</m:mo> <m:mi>h</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> left(G,h) -shadowing property in metric <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>G</m:mi> </m:mat","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135448134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Like q q -calculus, Hahn calculus (or q,ω q,omega -calculus) is constructed by defining a difference derivative operator and an integral operator. The q,ω q,omega -analogs of the integral representations of the Laplace transform and related special functions, such as gamma and beta, are proposed in this article. Then, some basic properties similar to classical and q q -analogs are investigated. Finally, a few examples are given to solve q,ω q,omega -initial value problems via the newly introduced q,ω q,omega -Laplace transform.
{"title":"Hahn Laplace transform and its applications","authors":"Fatma Hıra","doi":"10.1515/dema-2023-0259","DOIUrl":"https://doi.org/10.1515/dema-2023-0259","url":null,"abstract":"Abstract Like <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>q</m:mi> </m:math> q -calculus, Hahn calculus (or <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>q</m:mi> <m:mo>,</m:mo> <m:mi>ω</m:mi> </m:math> q,omega -calculus) is constructed by defining a difference derivative operator and an integral operator. The <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>q</m:mi> <m:mo>,</m:mo> <m:mi>ω</m:mi> </m:math> q,omega -analogs of the integral representations of the Laplace transform and related special functions, such as gamma and beta, are proposed in this article. Then, some basic properties similar to classical and <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>q</m:mi> </m:math> q -analogs are investigated. Finally, a few examples are given to solve <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>q</m:mi> <m:mo>,</m:mo> <m:mi>ω</m:mi> </m:math> q,omega -initial value problems via the newly introduced <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>q</m:mi> <m:mo>,</m:mo> <m:mi>ω</m:mi> </m:math> q,omega -Laplace transform.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135953599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Siriluk Paokanta, Mehdi Dehghanian, Choonkil Park, Y. Sayyari
Abstract In this article, we solve the system of additive functional equations: 2 f ( x + y ) − g ( x ) = g ( y ) , g ( x + y ) − 2 f ( y − x ) = 4 f ( x ) left{phantom{rule[-1.25em]{}{0ex}}begin{array}{l}2fleft(x+y)-gleft(x)=g(y), gleft(x+y)-2f(y-x)=4fleft(x)end{array}right. and prove the Hyers-Ulam stability of the system of additive functional equations in complex Banach spaces. Furthermore, we prove the Hyers-Ulam stability of f f -hom-ders in Banach algebras.
{"title":"A system of additive functional equations in complex Banach algebras","authors":"Siriluk Paokanta, Mehdi Dehghanian, Choonkil Park, Y. Sayyari","doi":"10.1515/dema-2022-0165","DOIUrl":"https://doi.org/10.1515/dema-2022-0165","url":null,"abstract":"Abstract In this article, we solve the system of additive functional equations: 2 f ( x + y ) − g ( x ) = g ( y ) , g ( x + y ) − 2 f ( y − x ) = 4 f ( x ) left{phantom{rule[-1.25em]{}{0ex}}begin{array}{l}2fleft(x+y)-gleft(x)=g(y), gleft(x+y)-2f(y-x)=4fleft(x)end{array}right. and prove the Hyers-Ulam stability of the system of additive functional equations in complex Banach spaces. Furthermore, we prove the Hyers-Ulam stability of f f -hom-ders in Banach algebras.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41579852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The Laplace transform method is applied in this article to study the semi-Hyers-Ulam-Rassias stability of a Volterra integro-differential equation of order n, with convolution-type kernel. This kind of stability extends the original Hyers-Ulam stability whose study originated in 1940. A general integral equation is formulated first, and then some particular cases (polynomial function and exponential function) for the function from the kernel are considered.
{"title":"Semi-Hyers-Ulam-Rassias stability for an integro-differential equation of order 𝓃","authors":"D. Inoan, D. Marian","doi":"10.1515/dema-2022-0198","DOIUrl":"https://doi.org/10.1515/dema-2022-0198","url":null,"abstract":"Abstract The Laplace transform method is applied in this article to study the semi-Hyers-Ulam-Rassias stability of a Volterra integro-differential equation of order n, with convolution-type kernel. This kind of stability extends the original Hyers-Ulam stability whose study originated in 1940. A general integral equation is formulated first, and then some particular cases (polynomial function and exponential function) for the function from the kernel are considered.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43534986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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