Pub Date : 2024-09-19DOI: 10.1186/s13660-024-03204-3
Lili Wan
In this paper, we discuss the fractional $p(x,cdot )$ -Kirchhoff-type equations $$ Mleft (int _{mathbb{R}^{N}times mathbb{R}^{N}} frac{1}{p(x,y)} frac{|u(x)-u(y)|^{p(x,y)}}{|x-y|^{N+sp(x,y)}}dxdyright )(-Delta _{p(x,.)})^{s} u+|u|^{bar{p}(x)-2}u=f(x,u).$$ We weaken the conditions on the nonlinear term f and get the existence and multiplicity of solutions via variational methods, which improves some previous results.
{"title":"Solutions for fractional (p(x,cdot ))-Kirchhoff-type equations in (mathbb{R}^{N})","authors":"Lili Wan","doi":"10.1186/s13660-024-03204-3","DOIUrl":"https://doi.org/10.1186/s13660-024-03204-3","url":null,"abstract":"In this paper, we discuss the fractional $p(x,cdot )$ -Kirchhoff-type equations $$ Mleft (int _{mathbb{R}^{N}times mathbb{R}^{N}} frac{1}{p(x,y)} frac{|u(x)-u(y)|^{p(x,y)}}{|x-y|^{N+sp(x,y)}}dxdyright )(-Delta _{p(x,.)})^{s} u+|u|^{bar{p}(x)-2}u=f(x,u).$$ We weaken the conditions on the nonlinear term f and get the existence and multiplicity of solutions via variational methods, which improves some previous results.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142267937","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}
Pub Date : 2024-09-16DOI: 10.1186/s13660-024-03202-5
Nizar Kh. Al-Oushoush, Laith E. Azar, Essam Awwad, Mario Krnić, Ahmed I. Saied
Motivated by certain results known from the literature, in this paper we give several new dynamic inequalities for B-monotone functions with respect to time scales nabla calculus. If the time scale represents the set of real numbers, our results reduce to integral inequalities known from the literature. On the other hand, in the setting of positive integers, we obtain new discrete inequalities for B-monotone sequences.
受文献中某些已知结果的启发，我们在本文中给出了关于时间尺度 nabla 微积分的 B 单调函数的几个新的动态不等式。如果时间尺度代表实数集，我们的结果就简化为文献中已知的积分不等式。另一方面，在正整数环境中，我们得到了 B 单调序列的新离散不等式。
{"title":"Some new dynamic inequalities for B-monotone functions with respect to time scales nabla calculus","authors":"Nizar Kh. Al-Oushoush, Laith E. Azar, Essam Awwad, Mario Krnić, Ahmed I. Saied","doi":"10.1186/s13660-024-03202-5","DOIUrl":"https://doi.org/10.1186/s13660-024-03202-5","url":null,"abstract":"Motivated by certain results known from the literature, in this paper we give several new dynamic inequalities for B-monotone functions with respect to time scales nabla calculus. If the time scale represents the set of real numbers, our results reduce to integral inequalities known from the literature. On the other hand, in the setting of positive integers, we obtain new discrete inequalities for B-monotone sequences.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142267938","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}
Pub Date : 2024-09-12DOI: 10.1186/s13660-024-03201-6
Mansour Shrahili
This paper considers parallel and series systems with heterogeneous components having dependent exponential lifetimes. The underlying dependence is assumed to be Archimedean and the component lifetimes are supposed to be connected according to an Archimedean copula. Sufficient conditions are found to dominate a parallel system with heterogenous exponential components, with respect to the dispersive order, by another parallel system with homogenous exponential components where the dependence structure between lifetimes of components is the same. We also compare two series systems (and two parallel systems) with general one-parameter dependent components and with respect to the usual stochastic ordering. Examples are given to illustrate the theoretical findings.
{"title":"Stochastic ordering results on extreme order statistics from dependent samples with Archimedean copula","authors":"Mansour Shrahili","doi":"10.1186/s13660-024-03201-6","DOIUrl":"https://doi.org/10.1186/s13660-024-03201-6","url":null,"abstract":"This paper considers parallel and series systems with heterogeneous components having dependent exponential lifetimes. The underlying dependence is assumed to be Archimedean and the component lifetimes are supposed to be connected according to an Archimedean copula. Sufficient conditions are found to dominate a parallel system with heterogenous exponential components, with respect to the dispersive order, by another parallel system with homogenous exponential components where the dependence structure between lifetimes of components is the same. We also compare two series systems (and two parallel systems) with general one-parameter dependent components and with respect to the usual stochastic ordering. Examples are given to illustrate the theoretical findings.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226532","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}
Pub Date : 2024-09-12DOI: 10.1186/s13660-024-03200-7
Amina Chaili, Abderrahmane Beniani, Ahmed Bchatnia, Suleman Alfalqi
In this paper, we investigate a system of coupled wave equations featuring boundary fractional damping applied to a portion of the domain. We first establish the well-posedness of the system, proving the existence and uniqueness of solutions through semi-group theory. While the system does not exhibit exponential stability, we demonstrate its strong stability. Furthermore, leveraging Arendt and Batty’s general criteria and certain geometric conditions, we prove a polynomial rate of energy decay for the solutions.
{"title":"Polynomial decay of the energy of solutions of coupled wave equations with locally boundary fractional dissipation","authors":"Amina Chaili, Abderrahmane Beniani, Ahmed Bchatnia, Suleman Alfalqi","doi":"10.1186/s13660-024-03200-7","DOIUrl":"https://doi.org/10.1186/s13660-024-03200-7","url":null,"abstract":"In this paper, we investigate a system of coupled wave equations featuring boundary fractional damping applied to a portion of the domain. We first establish the well-posedness of the system, proving the existence and uniqueness of solutions through semi-group theory. While the system does not exhibit exponential stability, we demonstrate its strong stability. Furthermore, leveraging Arendt and Batty’s general criteria and certain geometric conditions, we prove a polynomial rate of energy decay for the solutions.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209592","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}
Pub Date : 2024-09-11DOI: 10.1186/s13660-024-03198-y
Mohamed Kayid, Mashael A. Alshehri
This paper studies some stochastic properties of random quantiles according to the newly defined reliability measure called reversed aging intensity function. Preservation property of reversed aging intensity order under random quantile is obtained and using it, a lower bound and an upper bound for the reversed aging intensity function of a random quantile are derived. Preservation of two related monotonic reliability classes under random quantiles is also studied. We finally apply our results for reliability analysis of series systems with heterogeneous component lifetimes. Examples are included to examine and analyze the obtained results.
{"title":"Stochastic aspects of reversed aging intensity function of random quantiles","authors":"Mohamed Kayid, Mashael A. Alshehri","doi":"10.1186/s13660-024-03198-y","DOIUrl":"https://doi.org/10.1186/s13660-024-03198-y","url":null,"abstract":"This paper studies some stochastic properties of random quantiles according to the newly defined reliability measure called reversed aging intensity function. Preservation property of reversed aging intensity order under random quantile is obtained and using it, a lower bound and an upper bound for the reversed aging intensity function of a random quantile are derived. Preservation of two related monotonic reliability classes under random quantiles is also studied. We finally apply our results for reliability analysis of series systems with heterogeneous component lifetimes. Examples are included to examine and analyze the obtained results.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209578","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}
Pub Date : 2024-09-06DOI: 10.1186/s13660-024-03191-5
Rong Jin, Xufei Tang, Kan Chen
This article examines the strong consistency of the conditional value-at-risk (CVaR) estimate for asymptotic negatively associated (ANA or $rho ^{-}$ , for short) random samples under mild conditions. It is demonstrated that the optimal rate can achieve nearly $O (n^{-1/2})$ under certain appropriate conditions. Furthermore, we present numerical simulations and a real data example to corroborate our theoretical results based on finite samples.
{"title":"Asymptotic properties of conditional value-at-risk estimate for asymptotic negatively associated samples","authors":"Rong Jin, Xufei Tang, Kan Chen","doi":"10.1186/s13660-024-03191-5","DOIUrl":"https://doi.org/10.1186/s13660-024-03191-5","url":null,"abstract":"This article examines the strong consistency of the conditional value-at-risk (CVaR) estimate for asymptotic negatively associated (ANA or $rho ^{-}$ , for short) random samples under mild conditions. It is demonstrated that the optimal rate can achieve nearly $O (n^{-1/2})$ under certain appropriate conditions. Furthermore, we present numerical simulations and a real data example to corroborate our theoretical results based on finite samples.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209579","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}
Pub Date : 2024-09-05DOI: 10.1186/s13660-024-03188-0
Bahram Agheli, Rahmat Darzi
In this paper, we have explored the existence and uniqueness of solutions for a pair of nonlinear fractional integro-differential equations comprising of the Ψ-Caputo fractional derivative and the Ψ-Riemann–Liouville fractional integral. These equations are subject to nonlocal boundary conditions and a variable coefficient. Our findings are drawn upon the Mittage–Leffler function, Babenko’s attitude, and topological degree theory for condensing maps and the Banach contraction principle. To further elucidate our principal outcomes, we have presented two illustrative examples.
{"title":"New attitude on sequential Ψ-Caputo differential equations via concept of measures of noncompactness","authors":"Bahram Agheli, Rahmat Darzi","doi":"10.1186/s13660-024-03188-0","DOIUrl":"https://doi.org/10.1186/s13660-024-03188-0","url":null,"abstract":"In this paper, we have explored the existence and uniqueness of solutions for a pair of nonlinear fractional integro-differential equations comprising of the Ψ-Caputo fractional derivative and the Ψ-Riemann–Liouville fractional integral. These equations are subject to nonlocal boundary conditions and a variable coefficient. Our findings are drawn upon the Mittage–Leffler function, Babenko’s attitude, and topological degree theory for condensing maps and the Banach contraction principle. To further elucidate our principal outcomes, we have presented two illustrative examples.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209582","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}
Pub Date : 2024-09-05DOI: 10.1186/s13660-024-03197-z
Yang Liu, Long Wang, Yazheng Dang
In this research, we introduce a novel optimization algorithm termed the dual-relaxed inertial alternating direction method of multipliers (DR-IADM), tailored for handling nonconvex and nonsmooth problems. These problems are characterized by an objective function that is a composite of three elements: a smooth composite function combined with a linear operator, a nonsmooth function, and a mixed function of two variables. To facilitate the iterative process, we adopt a straightforward parameter selection approach, integrate inertial components within each subproblem, and introduce two relaxed terms to refine the dual variable update step. Within a set of reasonable assumptions, we establish the boundedness of the sequence generated by our DR-IADM algorithm. Furthermore, leveraging the Kurdyka–Łojasiewicz (KŁ) property, we demonstrate the global convergence of the proposed method. To validate the practicality and efficacy of our algorithm, we present numerical experiments that corroborate its performance. In summary, our contribution lies in proposing DR-IADM for a specific class of optimization problems, proving its convergence properties, and supporting the theoretical claims with numerical evidence.
{"title":"A modified inertial proximal alternating direction method of multipliers with dual-relaxed term for structured nonconvex and nonsmooth problem","authors":"Yang Liu, Long Wang, Yazheng Dang","doi":"10.1186/s13660-024-03197-z","DOIUrl":"https://doi.org/10.1186/s13660-024-03197-z","url":null,"abstract":"In this research, we introduce a novel optimization algorithm termed the dual-relaxed inertial alternating direction method of multipliers (DR-IADM), tailored for handling nonconvex and nonsmooth problems. These problems are characterized by an objective function that is a composite of three elements: a smooth composite function combined with a linear operator, a nonsmooth function, and a mixed function of two variables. To facilitate the iterative process, we adopt a straightforward parameter selection approach, integrate inertial components within each subproblem, and introduce two relaxed terms to refine the dual variable update step. Within a set of reasonable assumptions, we establish the boundedness of the sequence generated by our DR-IADM algorithm. Furthermore, leveraging the Kurdyka–Łojasiewicz (KŁ) property, we demonstrate the global convergence of the proposed method. To validate the practicality and efficacy of our algorithm, we present numerical experiments that corroborate its performance. In summary, our contribution lies in proposing DR-IADM for a specific class of optimization problems, proving its convergence properties, and supporting the theoretical claims with numerical evidence.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209580","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}
Pub Date : 2024-09-04DOI: 10.1186/s13660-024-03194-2
Samet Erden, Mehmet Zeki Sarıkaya, Burçin Gokkurt Ozdemir, Neslihan Uyanık
In this study, we firstly derive a Wirtinger-type result, which gives the connection in between the integral of square of a function and the integral of square of its Caputo fractional derivatives with the help of left-sided and right-sided fractional Taylor’s Formulas. Afterward, we provide a more general inequality involving Caputo fractional derivatives for $L_{r}$ norm with $r>1$ via Hölder’s inequality. Also, similar inequalities for Riemann–Liouville fractional derivatives are presented by means of a relation between Caputo fractional derivatives and Riemann–Liouville fractional derivatives.
{"title":"Wirtinger-type inequalities for Caputo fractional derivatives via Taylor’s formula","authors":"Samet Erden, Mehmet Zeki Sarıkaya, Burçin Gokkurt Ozdemir, Neslihan Uyanık","doi":"10.1186/s13660-024-03194-2","DOIUrl":"https://doi.org/10.1186/s13660-024-03194-2","url":null,"abstract":"In this study, we firstly derive a Wirtinger-type result, which gives the connection in between the integral of square of a function and the integral of square of its Caputo fractional derivatives with the help of left-sided and right-sided fractional Taylor’s Formulas. Afterward, we provide a more general inequality involving Caputo fractional derivatives for $L_{r}$ norm with $r>1$ via Hölder’s inequality. Also, similar inequalities for Riemann–Liouville fractional derivatives are presented by means of a relation between Caputo fractional derivatives and Riemann–Liouville fractional derivatives.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209581","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}
Let A, B, X, and Y be $ntimes n$ complex matrices such that A is self-adjoint, $Bgeq 0$ , $pm Aleq B$ , $max ( Vert X Vert ^{2}, Vert Y Vert ^{2} ) leq 1$ , and let f be a nonnegative increasing convex function on $[ 0,infty ) $ satisfying $f(0)=0$ . Then $$ 2s_{j}bigl(f bigl( biglvert XAY^{ast } bigrvert bigr) bigr)leq max bigl{ Vert X Vert ^{2}, Vert Y Vert ^{2} bigr} s_{j}bigl(f(B+A)oplus f(B-A)bigr) $$ for $j=1,2,ldots,n$ . This singular value inequality extends an inequality of Audeh and Kittaneh. Several generalizations for singular value and norm inequalities of matrices are also given.
让 A, B, X 和 Y 是 $ntimes n$ 复数矩阵，使得 A 是自相关的，$Bgeq 0$ , $pm Aleq B$ , $max ( Vert X Vert ^{2}, Vert Y Vert ^{2} ) leq 1$ , 并让 f 是一个在 $[ 0,infty ) $ 上满足 $f(0)=0$ 的非负递增凸函数。Then $$ 2s_{j}bigl(f biglvert XAY^{ast } bigrvert bigr) bigr)leq max bigl{ Vert X Vert ^{2}, Vert Y Vert ^{2}.s_{j}bigl(f(B+A)oplus f(B-A)bigr) $$ for $j=1,2,ldots,n$ 。这个奇异值不等式扩展了 Audeh 和 Kittaneh 的不等式。此外，还给出了矩阵奇异值不等式和规范不等式的几种一般化。
{"title":"Singular value inequalities of matrices via increasing functions","authors":"Wasim Audeh, Anwar Al-Boustanji, Manal Al-Labadi, Raja’a Al-Naimi","doi":"10.1186/s13660-024-03193-3","DOIUrl":"https://doi.org/10.1186/s13660-024-03193-3","url":null,"abstract":"Let A, B, X, and Y be $ntimes n$ complex matrices such that A is self-adjoint, $Bgeq 0$ , $pm Aleq B$ , $max ( Vert X Vert ^{2}, Vert Y Vert ^{2} ) leq 1$ , and let f be a nonnegative increasing convex function on $[ 0,infty ) $ satisfying $f(0)=0$ . Then $$ 2s_{j}bigl(f bigl( biglvert XAY^{ast } bigrvert bigr) bigr)leq max bigl{ Vert X Vert ^{2}, Vert Y Vert ^{2} bigr} s_{j}bigl(f(B+A)oplus f(B-A)bigr) $$ for $j=1,2,ldots,n$ . This singular value inequality extends an inequality of Audeh and Kittaneh. Several generalizations for singular value and norm inequalities of matrices are also given.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209589","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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