Abstract In this article, we have established some new bounds of Fejér-type Hermite-Hadamard inequality for k k -fractional integrals involving r r -times differentiable preinvex functions. It is noteworthy that in the past, there was no weighted version of the left and right sides of the Hermite-Hadamard inequality for k k -fractional integrals for generalized convex functions available in the literature.
{"title":"Weighted Hermite-Hadamard inequalities for r-times differentiable preinvex functions for k-fractional integrals","authors":"F. Zafar, S. Mehmood, A. Asiri","doi":"10.1515/dema-2022-0254","DOIUrl":"https://doi.org/10.1515/dema-2022-0254","url":null,"abstract":"Abstract In this article, we have established some new bounds of Fejér-type Hermite-Hadamard inequality for k k -fractional integrals involving r r -times differentiable preinvex functions. It is noteworthy that in the past, there was no weighted version of the left and right sides of the Hermite-Hadamard inequality for k k -fractional integrals for generalized convex functions available in the literature.","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":"48308078","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 We prove that if a self-affine arc γ ∈ R 2 gamma in {{mathbb{R}}}^{2} does not satisfy weak separation condition, then it is a segment of a parabola or a straight line. If a self-affine arc γ gamma is not a segment of a parabola or a line, then it is a component of the attractor of a Jordan multizipper with the same set of generators.
摘要证明了自仿射弧γ∈r2 gamma in {{mathbb{R}}}^{2}不满足弱分离条件，则它是抛物线或直线的一段。如果自仿射弧γ γ不是抛物线或直线的一段，则它是具有同一组生成器的Jordan多拉链的吸引子的一个分量。
{"title":"On the structure of self-affine Jordan arcs in ℝ2","authors":"A. Tetenov, Allanazar Kutlimuratov","doi":"10.1515/dema-2022-0228","DOIUrl":"https://doi.org/10.1515/dema-2022-0228","url":null,"abstract":"Abstract We prove that if a self-affine arc γ ∈ R 2 gamma in {{mathbb{R}}}^{2} does not satisfy weak separation condition, then it is a segment of a parabola or a straight line. If a self-affine arc γ gamma is not a segment of a parabola or a line, then it is a component of the attractor of a Jordan multizipper with the same set of generators.","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":"48719458","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 define the following: Let N 0 {{mathbb{N}}}_{0} be the set of all nonnegative integers and D = ( d i ) i ∈ N 0 D={left({d}_{i})}_{iin {{mathbb{N}}}_{0}} a family of additive mappings of a ∗ ast -ring R R such that d 0 = i d R {d}_{0}=i{d}_{R} . D D is called a Jordan ( α , β ) left(alpha ,beta ) -higher ∗ ast -derivation (resp. a Jordan triple ( α , β ) left(alpha ,beta ) -higher ∗ ast -derivation) of R R if d n ( a 2 ) = ∑ i + j = n d i ( β j ( a ) ) d j ( α i ( a ∗ i ) ) {d}_{n}left({a}^{2})={sum }_{i+j=n}{d}_{i}left({beta }^{j}left(a)){d}_{j}left({alpha }^{i}left({a}^{{ast }^{i}})) (resp. d n ( a b a ) = ∑ i + j + k = n d i ( β j + k ( a ) ) d j ( β k ( α i ( b ∗ i ) ) ) d k ( α i + j ( a ∗ i + j ) ) {d}_{n}left(aba)={sum }_{i+j+k=n}{d}_{i}left({beta }^{j+k}left(a)){d}_{j}left({beta }^{k}left({alpha }^{i}left({b}^{{ast }^{i}}))){d}_{k}left({alpha }^{i+j}left({a}^{{ast }^{i+j}})) ) for all a , b ∈ R a,bin R and each n ∈ N 0 nin {{mathbb{N}}}_{0} . We show that the two notions of Jordan ( α , β ) left(alpha ,beta ) -higher ∗ ast -derivation and Jordan triple ( α , β ) left(alpha ,beta ) -higher ∗ ast -derivation on a 6-torsion free semiprime ∗ ast -ring are equivalent.
在本文中，我们定义如下:设N为0 {{mathbb{N}}}＿{0} 为所有非负整数的集合，且D= (d1) i∈n0 D={left（{d}＿{I}）}＿{Iin {{mathbb{N}}}＿{0}} A *的一组可加映射 ast -环R R使得d0 = i d R {d}＿{0}= 1{d}＿{r} 。D D被称为约当(α， β) left（alpha ，beta ) -较高* ast - derivative(衍生)Jordan三重(α， β) left（alpha ，beta ) -较高* ast 如果d n (a 2) =∑i + j = n d i (β j (a)) d j (α i (a * i)) {d}＿{n}left（{a}＾{2}）={sum }＿{i+j=n}{d}＿{I}left（{beta }＾{j}left(a)){d}＿{j}left（{alpha }＾{I}left（{a}＾{{ast }＾{I}})(回答;回答D n (a b a) =∑I + j + k = n D I (β j + k (a)) D j (β k (α I (b∗I))) D k (α I + j (a∗I + j))) {d}＿{n}left(aba)={sum }＿{i+j+k=n}{d}＿{I}left（{beta }＾{j+k}left(a)){d}＿{j}left（{beta }＾{k}left（{alpha }＾{I}left（{b}＾{{ast }＾{I}}））){d}＿{k}left（{alpha }＾{i+j}left（{a}＾{{ast }＾{i+j}})))对于所有a,b∈R a,bin R和每个n∈n0nin {{mathbb{N}}}＿{0} 。我们证明了Jordan (α， β)的两个概念 left（alpha ，beta ) -较高* ast -衍生和Jordan三重(α， β) left（alpha ，beta ) -较高* ast 6-无扭转半素数*上的导数 ast -环是等价的。
{"title":"Jordan triple (α,β)-higher ∗-derivations on semiprime rings","authors":"O. H. Ezzat","doi":"10.1515/dema-2022-0213","DOIUrl":"https://doi.org/10.1515/dema-2022-0213","url":null,"abstract":"Abstract In this article, we define the following: Let N 0 {{mathbb{N}}}_{0} be the set of all nonnegative integers and D = ( d i ) i ∈ N 0 D={left({d}_{i})}_{iin {{mathbb{N}}}_{0}} a family of additive mappings of a ∗ ast -ring R R such that d 0 = i d R {d}_{0}=i{d}_{R} . D D is called a Jordan ( α , β ) left(alpha ,beta ) -higher ∗ ast -derivation (resp. a Jordan triple ( α , β ) left(alpha ,beta ) -higher ∗ ast -derivation) of R R if d n ( a 2 ) = ∑ i + j = n d i ( β j ( a ) ) d j ( α i ( a ∗ i ) ) {d}_{n}left({a}^{2})={sum }_{i+j=n}{d}_{i}left({beta }^{j}left(a)){d}_{j}left({alpha }^{i}left({a}^{{ast }^{i}})) (resp. d n ( a b a ) = ∑ i + j + k = n d i ( β j + k ( a ) ) d j ( β k ( α i ( b ∗ i ) ) ) d k ( α i + j ( a ∗ i + j ) ) {d}_{n}left(aba)={sum }_{i+j+k=n}{d}_{i}left({beta }^{j+k}left(a)){d}_{j}left({beta }^{k}left({alpha }^{i}left({b}^{{ast }^{i}}))){d}_{k}left({alpha }^{i+j}left({a}^{{ast }^{i+j}})) ) for all a , b ∈ R a,bin R and each n ∈ N 0 nin {{mathbb{N}}}_{0} . We show that the two notions of Jordan ( α , β ) left(alpha ,beta ) -higher ∗ ast -derivation and Jordan triple ( α , β ) left(alpha ,beta ) -higher ∗ ast -derivation on a 6-torsion free semiprime ∗ ast -ring are equivalent.","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":"41839843","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 Kirchhoff model is derived from the vibration problem of stretchable strings. This article focuses on the long-time dynamics of a class of higher-order coupled Kirchhoff systems with nonlinear strong damping. The existence and uniqueness of the solutions of these equations in different spaces are proved by prior estimation and the Faedo-Galerkin method. Subsequently, the family of global attractors of these problems is proved using the compactness theorem. In this article, we systematically propose the definition and proof process of the family of global attractors and enrich the related conclusions of higher-order coupled Kirchhoff models. The conclusions lay a theoretical foundation for future practical applications.
{"title":"The asymptotic behaviors of solutions for higher-order (m1, m2)-coupled Kirchhoff models with nonlinear strong damping","authors":"Penghui Lv, Guoguang Lin, Xiaojun Lv","doi":"10.1515/dema-2022-0197","DOIUrl":"https://doi.org/10.1515/dema-2022-0197","url":null,"abstract":"Abstract The Kirchhoff model is derived from the vibration problem of stretchable strings. This article focuses on the long-time dynamics of a class of higher-order coupled Kirchhoff systems with nonlinear strong damping. The existence and uniqueness of the solutions of these equations in different spaces are proved by prior estimation and the Faedo-Galerkin method. Subsequently, the family of global attractors of these problems is proved using the compactness theorem. In this article, we systematically propose the definition and proof process of the family of global attractors and enrich the related conclusions of higher-order coupled Kirchhoff models. The conclusions lay a theoretical foundation for future practical applications.","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":"46954030","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 classification of the phase portraits is one of the classical and difficult problems in the qualitative theory of polynomial differential systems in R 2 {{mathbb{R}}}^{2} , particularly for quadratic systems. Even with the hundreds of studies on the topology of real planar quadratic vector fields, fully characterizing their phase portraits is still a difficult problem. This paper is devoted to classifying the phase portraits of two polynomial vector fields with two usual invariant algebraic curves, by investigating the geometric solutions within the Poincaré disc. One can notice that these systems yield 26 topologically different phase portraits.
{"title":"Phase portraits of two classes of quadratic differential systems exhibiting as solutions two cubic algebraic curves","authors":"R. Benterki, Ahlam Belfar","doi":"10.1515/dema-2022-0218","DOIUrl":"https://doi.org/10.1515/dema-2022-0218","url":null,"abstract":"Abstract The classification of the phase portraits is one of the classical and difficult problems in the qualitative theory of polynomial differential systems in R 2 {{mathbb{R}}}^{2} , particularly for quadratic systems. Even with the hundreds of studies on the topology of real planar quadratic vector fields, fully characterizing their phase portraits is still a difficult problem. This paper is devoted to classifying the phase portraits of two polynomial vector fields with two usual invariant algebraic curves, by investigating the geometric solutions within the Poincaré disc. One can notice that these systems yield 26 topologically different phase portraits.","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":"48541728","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, a class of cyclic (noncyclic) operators are defined on Banach spaces via concept of measure of noncompactness using some abstract functions. The best proximity point (pair) results are manifested for the said operators. The obtained main results are applied to demonstrate the existence of optimum solutions of a system of fractional differential equations involving ( k , ψ ) left(k,psi ) -Hilfer fractional derivatives.
{"title":"Global optimum solutions for a system of (k, ψ)-Hilfer fractional differential equations: Best proximity point approach","authors":"P. Patle, M. Gabeleh, M. de La Sen","doi":"10.1515/dema-2022-0253","DOIUrl":"https://doi.org/10.1515/dema-2022-0253","url":null,"abstract":"Abstract In this article, a class of cyclic (noncyclic) operators are defined on Banach spaces via concept of measure of noncompactness using some abstract functions. The best proximity point (pair) results are manifested for the said operators. The obtained main results are applied to demonstrate the existence of optimum solutions of a system of fractional differential equations involving ( k , ψ ) left(k,psi ) -Hilfer fractional derivatives.","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":"42883235","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 Let G G be a group and R R be a G G -graded commutative ring with nonzero unity 1. In this article, we introduce the concept of graded weakly 1-absorbing primary ideals which is a generalization of graded 1-absorbing primary ideal. A proper graded ideal P P of R R is said to be a graded weakly 1-absorbing primary ideal of R R if whenever nonunit elements x , y , z ∈ h ( R ) x,y,zin hleft(R) such that 0 ≠ x y z ∈ P 0ne xyzin P , then x y ∈ P xyin P or z n ∈ P {z}^{n}in P , for some n ∈ N nin {mathbb{N}} . Several properties of graded weakly 1-absorbing primary ideals are investigated.
{"title":"Graded weakly 1-absorbing primary ideals","authors":"M. Bataineh, R. Abu-Dawwas","doi":"10.1515/dema-2022-0214","DOIUrl":"https://doi.org/10.1515/dema-2022-0214","url":null,"abstract":"Abstract Let G G be a group and R R be a G G -graded commutative ring with nonzero unity 1. In this article, we introduce the concept of graded weakly 1-absorbing primary ideals which is a generalization of graded 1-absorbing primary ideal. A proper graded ideal P P of R R is said to be a graded weakly 1-absorbing primary ideal of R R if whenever nonunit elements x , y , z ∈ h ( R ) x,y,zin hleft(R) such that 0 ≠ x y z ∈ P 0ne xyzin P , then x y ∈ P xyin P or z n ∈ P {z}^{n}in P , for some n ∈ N nin {mathbb{N}} . Several properties of graded weakly 1-absorbing primary ideals are investigated.","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":"67144060","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 study the regularity criteria of the weak solutions to the Boussinesq equations involving the horizontal component of velocity or the horizontal derivatives of the two components of velocity in anisotropic Lorentz spaces. This result reveals that the velocity field plays a dominant role in regularity theory of the Boussinesq equations.
{"title":"Regularity criteria via horizontal component of velocity for the Boussinesq equations in anisotropic Lorentz spaces","authors":"R. Agarwal, Ahmad M. Alghamdi, S. Gala, M. Ragusa","doi":"10.1515/dema-2022-0221","DOIUrl":"https://doi.org/10.1515/dema-2022-0221","url":null,"abstract":"Abstract In this article, we study the regularity criteria of the weak solutions to the Boussinesq equations involving the horizontal component of velocity or the horizontal derivatives of the two components of velocity in anisotropic Lorentz spaces. This result reveals that the velocity field plays a dominant role in regularity theory of the Boussinesq equations.","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":"46151945","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 1970s, Rota began to build completely rigid foundations for the theory of umbral calculus based on relatively modern ideas of linear functions and linear operators. Since then, umbral calculus has been used in the study of special functions in various fields. In this article, we derive some new and interesting identities related to degenerate derangement polynomials and some special polynomials by using λ lambda -Sheffer sequences and λ lambda -umbral calculus, which are defined by Kim-Kim (Degenerate Sheffer sequences and λ lambda -Sheffer sequences, J. Math. Anal. Appl. 493 (2021), 124521, 21pp).
{"title":"Study of degenerate derangement polynomials by λ-umbral calculus","authors":"S. Yun, Jin-Woo Park","doi":"10.1515/dema-2022-0240","DOIUrl":"https://doi.org/10.1515/dema-2022-0240","url":null,"abstract":"Abstract In the 1970s, Rota began to build completely rigid foundations for the theory of umbral calculus based on relatively modern ideas of linear functions and linear operators. Since then, umbral calculus has been used in the study of special functions in various fields. In this article, we derive some new and interesting identities related to degenerate derangement polynomials and some special polynomials by using λ lambda -Sheffer sequences and λ lambda -umbral calculus, which are defined by Kim-Kim (Degenerate Sheffer sequences and λ lambda -Sheffer sequences, J. Math. Anal. Appl. 493 (2021), 124521, 21pp).","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":"47065584","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 paradigm of choice practice represents the psychological theory of learning in the development of moral judgment. It is concerned with evaluating the implications of several choices and selecting one of them to implement. The goal of this work is to provide a generic functional equation to observe the behavior of animals in such circumstances. Our suggested functional equation can be employed to describe several well-known psychology and learning theories. The fixed point theorem proposed by Banach is utilized to show that the solution of a given functional problem exists and is unique. In addition, the stability of the given functional equation’s solution is discussed in terms of the Hyers-Ulam and Hyers-Ulam-Rassias results. Furthermore, two examples are provided to highlight the relevance of the significant outcomes in the context of the literature.
{"title":"The existence and uniqueness of solutions to a functional equation arising in psychological learning theory","authors":"A. Turab, N. Rosli, Wajahat Ali, J. Nieto","doi":"10.1515/dema-2022-0231","DOIUrl":"https://doi.org/10.1515/dema-2022-0231","url":null,"abstract":"Abstract The paradigm of choice practice represents the psychological theory of learning in the development of moral judgment. It is concerned with evaluating the implications of several choices and selecting one of them to implement. The goal of this work is to provide a generic functional equation to observe the behavior of animals in such circumstances. Our suggested functional equation can be employed to describe several well-known psychology and learning theories. The fixed point theorem proposed by Banach is utilized to show that the solution of a given functional problem exists and is unique. In addition, the stability of the given functional equation’s solution is discussed in terms of the Hyers-Ulam and Hyers-Ulam-Rassias results. Furthermore, two examples are provided to highlight the relevance of the significant outcomes in the context of the literature.","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":"47802851","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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