Abstract In this article, we introduce and study the notion of split generalized equilibrium problem with multiple output sets (SGEPMOS). We propose a new iterative method that employs viscosity approximation technique for approximating the common solution of the SGEPMOS and common fixed point problem for an infinite family of multivalued demicontractive mappings in real Hilbert spaces. Under mild conditions, we prove a strong convergence theorem for the proposed method. Our method uses self-adaptive step size that does not require prior knowledge of the operator norm. The results presented in this article unify, complement, and extend several existing recent results in the literature.
{"title":"On split generalized equilibrium problem with multiple output sets and common fixed points problem","authors":"E. C. Godwin, O. Mewomo, T. O. Alakoya","doi":"10.1515/dema-2022-0251","DOIUrl":"https://doi.org/10.1515/dema-2022-0251","url":null,"abstract":"Abstract In this article, we introduce and study the notion of split generalized equilibrium problem with multiple output sets (SGEPMOS). We propose a new iterative method that employs viscosity approximation technique for approximating the common solution of the SGEPMOS and common fixed point problem for an infinite family of multivalued demicontractive mappings in real Hilbert spaces. Under mild conditions, we prove a strong convergence theorem for the proposed method. Our method uses self-adaptive step size that does not require prior knowledge of the operator norm. The results presented in this article unify, complement, and extend several existing recent results 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":"47645313","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 nonlinear fractional-order cubic-quintic-heptic Duffing problem will be solved through a new numerical approximation technique. The suggested method is based on the Pell-Lucas polynomials’ operational matrix in the fractional and integer orders. The studied problem will be transformed into a nonlinear system of algebraic equations. The numerical expansion containing unknown coefficients will be obtained numerically via applying Newton’s iteration method to the claimed system. Convergence analysis and error estimates for the introduced process will be discussed. Numerical applications will be given to illustrate the applicability and accuracy of the proposed method.
{"title":"Pell-Lucas polynomials for numerical treatment of the nonlinear fractional-order Duffing equation","authors":"A. A. El-Sayed","doi":"10.1515/dema-2022-0220","DOIUrl":"https://doi.org/10.1515/dema-2022-0220","url":null,"abstract":"Abstract The nonlinear fractional-order cubic-quintic-heptic Duffing problem will be solved through a new numerical approximation technique. The suggested method is based on the Pell-Lucas polynomials’ operational matrix in the fractional and integer orders. The studied problem will be transformed into a nonlinear system of algebraic equations. The numerical expansion containing unknown coefficients will be obtained numerically via applying Newton’s iteration method to the claimed system. Convergence analysis and error estimates for the introduced process will be discussed. Numerical applications will be given to illustrate the applicability and accuracy of the proposed 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":"47765589","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}
P. Charoensawan, Supreedee Dangskul, P. Varnakovida
Abstract This article introduces a type of dominating property, partially inherited from L. Chen’s, and proves an existence and uniqueness theorem concerning common best proximity points. A certain kind of boundary value problem involving the so-called Caputo derivative can be formulated so that our result applies.
{"title":"Common best proximity points for a pair of mappings with certain dominating property","authors":"P. Charoensawan, Supreedee Dangskul, P. Varnakovida","doi":"10.1515/dema-2022-0215","DOIUrl":"https://doi.org/10.1515/dema-2022-0215","url":null,"abstract":"Abstract This article introduces a type of dominating property, partially inherited from L. Chen’s, and proves an existence and uniqueness theorem concerning common best proximity points. A certain kind of boundary value problem involving the so-called Caputo derivative can be formulated so that our result applies.","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":"43984511","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 investigate the relationships between the instantaneous invariants of a one-parameter spatial movement and the local invariants of the axodes. Specifically, we provide new proofs for the Euler-Savary and Disteli formulas using the E. Study map in spatial kinematics, showcasing its elegance and efficiency. In addition, we introduce two line congruences and thoroughly analyze their spatial equivalence. Our findings contribute to a deeper understanding of the interplay between spatial movements and axodes, with potential applications in fields such as robotics and mechanical engineering.
{"title":"Kinematic-geometry of a line trajectory and the invariants of the axodes","authors":"Yanlin Li, Fatemah Mofarreh, Rashad A. Abdel-Baky","doi":"10.1515/dema-2022-0252","DOIUrl":"https://doi.org/10.1515/dema-2022-0252","url":null,"abstract":"Abstract In this article, we investigate the relationships between the instantaneous invariants of a one-parameter spatial movement and the local invariants of the axodes. Specifically, we provide new proofs for the Euler-Savary and Disteli formulas using the E. Study map in spatial kinematics, showcasing its elegance and efficiency. In addition, we introduce two line congruences and thoroughly analyze their spatial equivalence. Our findings contribute to a deeper understanding of the interplay between spatial movements and axodes, with potential applications in fields such as robotics and mechanical engineering.","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":"135181565","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 aim of this article is to present some novel geometric properties for three distinct normalizations of the generalized k k -Bessel functions, such as the radii of uniform convexity and of α alpha -convexity. In addition, we show that the radii of α alpha -convexity remain in between the radii of starlikeness and convexity, in the case when α ∈ [ 0 , 1 ] , alpha in {[}0,1], and they are decreasing with respect to the parameter α . alpha . The key tools in the proof of our main results are infinite product representations for normalized k k -Bessel functions and some properties of real zeros of these functions.
{"title":"On some geometric results for generalized k-Bessel functions","authors":"Evrim Toklu","doi":"10.1515/dema-2022-0235","DOIUrl":"https://doi.org/10.1515/dema-2022-0235","url":null,"abstract":"Abstract The main aim of this article is to present some novel geometric properties for three distinct normalizations of the generalized k k -Bessel functions, such as the radii of uniform convexity and of α alpha -convexity. In addition, we show that the radii of α alpha -convexity remain in between the radii of starlikeness and convexity, in the case when α ∈ [ 0 , 1 ] , alpha in {[}0,1], and they are decreasing with respect to the parameter α . alpha . The key tools in the proof of our main results are infinite product representations for normalized k k -Bessel functions and some properties of real zeros of these functions.","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":"41547161","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 investigate the existence and nonexistence of nonnegative radial solutions to exterior problems of the form Δ H m u ( q ) + λ ψ ( q ) K ( r ( q ) ) f ( r 2 − Q ( q ) , u ( q ) ) = 0 {Delta }_{{{mathbb{H}}}^{m}}uleft(q)+lambda psi left(q)Kleft(rleft(q))fleft({r}^{2-Q}left(q),uleft(q))=0 in B 1 c {B}_{1}^{c} , under the Dirichlet boundary conditions u = 0 u=0 on ∂ B 1 partial {B}_{1} and lim r ( q ) → ∞ u ( q ) = 0 {mathrm{lim}}_{rleft(q)to infty }uleft(q)=0 . Here, λ ≥ 0 lambda ge 0 is a parameter, Δ H m {Delta }_{{{mathbb{H}}}^{m}} is the Kohn Laplacian on the Heisenberg group H m = R 2 m + 1 {{mathbb{H}}}^{m}={{mathbb{R}}}^{2m+1} , m > 1 mgt 1 , Q = 2 m + 2 Q=2m+2 , B 1 {B}_{1} is the unit ball in H m {{mathbb{H}}}^{m} , B 1 c {B}_{1}^{c} is the complement of B 1 {B}_{1} , and ψ ( q ) = ∣ z ∣ 2 r 2 ( q ) psi left(q)=frac{| z{| }^{2}}{{r}^{2}left(q)} . Namely, under certain conditions on K K and f f , we show that there exists a critical parameter λ ∗ ∈ ( 0 , ∞ ] {lambda }^{ast }in left(0,infty ] in the following sense. If 0 ≤ λ < λ ∗ 0le lambda lt {lambda }^{ast } , the above problem admits a unique nonnegative radial solution u λ {u}_{lambda } ; if λ ∗ < ∞ {lambda }^{ast }lt infty and λ ≥ λ ∗ lambda ge {lambda }^{ast } , the problem admits no nonnegative radial solution. When 0 ≤ λ < λ ∗ 0le lambda lt {lambda }^{ast } , a numerical algorithm that converges to u λ {u}_{lambda } is provided and the continuity of u λ {u}_{lambda } with respect to λ lambda , as well as the behavior of u λ {u}_{lambda } as λ → λ ∗ − lambda to {{lambda }^{ast }}^{-} , are studied. Moreover, sufficient conditions on the the behavior of f ( t , s ) fleft(t,s) as s → ∞ sto infty are obtained, for which λ ∗ = ∞ {lambda }^{ast }=infty or λ ∗ < ∞ {lambda }^{ast }lt infty . Our approach is based on partial ordering methods and fixed point theory in cones.
{"title":"On the existence of nonnegative radial solutions for Dirichlet exterior problems on the Heisenberg group","authors":"M. Jleli","doi":"10.1515/dema-2022-0193","DOIUrl":"https://doi.org/10.1515/dema-2022-0193","url":null,"abstract":"Abstract We investigate the existence and nonexistence of nonnegative radial solutions to exterior problems of the form Δ H m u ( q ) + λ ψ ( q ) K ( r ( q ) ) f ( r 2 − Q ( q ) , u ( q ) ) = 0 {Delta }_{{{mathbb{H}}}^{m}}uleft(q)+lambda psi left(q)Kleft(rleft(q))fleft({r}^{2-Q}left(q),uleft(q))=0 in B 1 c {B}_{1}^{c} , under the Dirichlet boundary conditions u = 0 u=0 on ∂ B 1 partial {B}_{1} and lim r ( q ) → ∞ u ( q ) = 0 {mathrm{lim}}_{rleft(q)to infty }uleft(q)=0 . Here, λ ≥ 0 lambda ge 0 is a parameter, Δ H m {Delta }_{{{mathbb{H}}}^{m}} is the Kohn Laplacian on the Heisenberg group H m = R 2 m + 1 {{mathbb{H}}}^{m}={{mathbb{R}}}^{2m+1} , m > 1 mgt 1 , Q = 2 m + 2 Q=2m+2 , B 1 {B}_{1} is the unit ball in H m {{mathbb{H}}}^{m} , B 1 c {B}_{1}^{c} is the complement of B 1 {B}_{1} , and ψ ( q ) = ∣ z ∣ 2 r 2 ( q ) psi left(q)=frac{| z{| }^{2}}{{r}^{2}left(q)} . Namely, under certain conditions on K K and f f , we show that there exists a critical parameter λ ∗ ∈ ( 0 , ∞ ] {lambda }^{ast }in left(0,infty ] in the following sense. If 0 ≤ λ < λ ∗ 0le lambda lt {lambda }^{ast } , the above problem admits a unique nonnegative radial solution u λ {u}_{lambda } ; if λ ∗ < ∞ {lambda }^{ast }lt infty and λ ≥ λ ∗ lambda ge {lambda }^{ast } , the problem admits no nonnegative radial solution. When 0 ≤ λ < λ ∗ 0le lambda lt {lambda }^{ast } , a numerical algorithm that converges to u λ {u}_{lambda } is provided and the continuity of u λ {u}_{lambda } with respect to λ lambda , as well as the behavior of u λ {u}_{lambda } as λ → λ ∗ − lambda to {{lambda }^{ast }}^{-} , are studied. Moreover, sufficient conditions on the the behavior of f ( t , s ) fleft(t,s) as s → ∞ sto infty are obtained, for which λ ∗ = ∞ {lambda }^{ast }=infty or λ ∗ < ∞ {lambda }^{ast }lt infty . Our approach is based on partial ordering methods and fixed point theory in cones.","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":"49023204","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 Nonlocal operators with different kernels were used here to obtain more general harmonic oscillator models. Power law, exponential decay, and the generalized Mittag-Leffler kernels with Delta-Dirac property have been utilized in this process. The aim of this study was to introduce into the damped harmonic oscillator model nonlocalities associated with these mentioned kernels and see the effect of each one of them when computing the Bode diagram obtained from the Laplace and the Sumudu transform. For each case, we applied both the Laplace and the Sumudu transform to obtain a solution in a complex space. For each case, we obtained the Bode diagram and the phase diagram for different values of fractional orders. We presented a detailed analysis of uniqueness and an exact solution and used numerical approximation to obtain a numerical solution.
{"title":"Analytical and numerical analysis of damped harmonic oscillator model with nonlocal operators","authors":"N. Alharthi, A. Atangana, B. Alkahtani","doi":"10.1515/dema-2022-0230","DOIUrl":"https://doi.org/10.1515/dema-2022-0230","url":null,"abstract":"Abstract Nonlocal operators with different kernels were used here to obtain more general harmonic oscillator models. Power law, exponential decay, and the generalized Mittag-Leffler kernels with Delta-Dirac property have been utilized in this process. The aim of this study was to introduce into the damped harmonic oscillator model nonlocalities associated with these mentioned kernels and see the effect of each one of them when computing the Bode diagram obtained from the Laplace and the Sumudu transform. For each case, we applied both the Laplace and the Sumudu transform to obtain a solution in a complex space. For each case, we obtained the Bode diagram and the phase diagram for different values of fractional orders. We presented a detailed analysis of uniqueness and an exact solution and used numerical approximation to obtain a numerical solution.","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":"43076939","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 aim of this article is to investigate the neutrosophic Nörlund ℐ-statistically convergent sequence space. We present some neutrosophic normed spaces (NNSs) in Nörlund convergent spaces. In addition, we also examine various topological and algebraic properties of these convergent sequence spaces. Theorems are proved in light of the NNS theory approach. Results are obtained via different perspectives and new examples are produced to justify the counterparts and show the existence of the introduced notions. The results established in this research work supply an exhaustive foundation in NNS and make a significant contribution to the theoretical development of NNS in the literature. The original aspect of this study is the first wholly up-to-date and thorough examination of the features and implementation of neutrosophic Nörlund ℐ-statistically convergent sequences in NNS, based upon the standard definition.
{"title":"Certain aspects of Nörlund ℐ-statistical convergence of sequences in neutrosophic normed spaces","authors":"Ö. Kişi, M. Gürdal, Burak Çakal","doi":"10.1515/dema-2022-0194","DOIUrl":"https://doi.org/10.1515/dema-2022-0194","url":null,"abstract":"Abstract The aim of this article is to investigate the neutrosophic Nörlund ℐ-statistically convergent sequence space. We present some neutrosophic normed spaces (NNSs) in Nörlund convergent spaces. In addition, we also examine various topological and algebraic properties of these convergent sequence spaces. Theorems are proved in light of the NNS theory approach. Results are obtained via different perspectives and new examples are produced to justify the counterparts and show the existence of the introduced notions. The results established in this research work supply an exhaustive foundation in NNS and make a significant contribution to the theoretical development of NNS in the literature. The original aspect of this study is the first wholly up-to-date and thorough examination of the features and implementation of neutrosophic Nörlund ℐ-statistically convergent sequences in NNS, based upon the standard definition.","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":"46025153","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}
H. Rehman, P. Kumam, Murat Ozdemir, I. Yildirim, W. Kumam
Abstract The primary goal of this research is to investigate the approximate numerical solution of variational inequalities using quasimonotone operators in infinite-dimensional real Hilbert spaces. In this study, the sequence obtained by the proposed iterative technique for solving quasimonotone variational inequalities converges strongly toward a solution due to the viscosity-type iterative scheme. Furthermore, a new technique is proposed that uses an inertial mechanism to obtain strong convergence iteratively without the requirement for a hybrid version. The fundamental benefit of the suggested iterative strategy is that it substitutes a monotone and non-monotone step size rule based on mapping (operator) information for its Lipschitz constant or another line search method. This article also provides a numerical example to demonstrate how each method works.
{"title":"A class of strongly convergent subgradient extragradient methods for solving quasimonotone variational inequalities","authors":"H. Rehman, P. Kumam, Murat Ozdemir, I. Yildirim, W. Kumam","doi":"10.1515/dema-2022-0202","DOIUrl":"https://doi.org/10.1515/dema-2022-0202","url":null,"abstract":"Abstract The primary goal of this research is to investigate the approximate numerical solution of variational inequalities using quasimonotone operators in infinite-dimensional real Hilbert spaces. In this study, the sequence obtained by the proposed iterative technique for solving quasimonotone variational inequalities converges strongly toward a solution due to the viscosity-type iterative scheme. Furthermore, a new technique is proposed that uses an inertial mechanism to obtain strong convergence iteratively without the requirement for a hybrid version. The fundamental benefit of the suggested iterative strategy is that it substitutes a monotone and non-monotone step size rule based on mapping (operator) information for its Lipschitz constant or another line search method. This article also provides a numerical example to demonstrate how each method works.","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":"67143964","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 aim of this study is to investigate the boundedness, essential norm, and compactness of generalized Stević-Sharma operator from the minimal Möbius invariant space into Bloch-type space.
{"title":"Generalized Stević-Sharma operators from the minimal Möbius invariant space into Bloch-type spaces","authors":"Zhitao Guo","doi":"10.1515/dema-2022-0245","DOIUrl":"https://doi.org/10.1515/dema-2022-0245","url":null,"abstract":"Abstract The aim of this study is to investigate the boundedness, essential norm, and compactness of generalized Stević-Sharma operator from the minimal Möbius invariant space into Bloch-type space.","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":"135911676","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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