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Boundedness of commutators of variable Marcinkiewicz fractional integral operator in grand variable Herz spaces 大变赫兹空间中可变马钦凯维奇分数积分算子换元的有界性
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-07-11 DOI: 10.1186/s13660-024-03169-3
Babar Sultan, Mehvish Sultan, Aziz Khan, Thabet Abdeljawad
{"title":"Boundedness of commutators of variable Marcinkiewicz fractional integral operator in grand variable Herz spaces","authors":"Babar Sultan, Mehvish Sultan, Aziz Khan, Thabet Abdeljawad","doi":"10.1186/s13660-024-03169-3","DOIUrl":"https://doi.org/10.1186/s13660-024-03169-3","url":null,"abstract":"Let $mathbb{S}^{n-1}$ denote unit sphere in $mathbb{R}^{n}$ equipped with the normalized Lebesgue measure. Let $Phi in L^{s}(mathbb{S}^{n-1})$ be a homogeneous function of degree zero such that $int _{mathbb{S}^{n-1}}Phi (y^{prime})d sigma (y^{prime})=0$ , where $y^{prime}=y/|y|$ for any $yneq 0$ . The commutators of variable Marcinkiewicz fractional integral operator is defined as $$ [b,mu _{Phi}]^{m}_{beta }(f)(x )= left ( int limits _{0} ^{ infty }left |int limits _{|x -y | leq s} frac{Phi (x -y )[b(x )-b(y )]^{m}}{|x -y |^{n-1-beta (x )}}f(y )dy right |^{2} frac{ds}{s^{3}}right )^{frac{1}{2}}. $$ In this paper, we obtain the boundedness of the commutators of the variable Marcinkiewicz fractional integral operator on grand variable Herz spaces ${dot{K} ^{alpha (cdot ), q),theta}_{ p(cdot )}(mathbb{R}^{n})}$ .","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"27 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141588607","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}
引用次数: 0
Common best proximity point theorems in Hausdorff topological spaces 豪斯多夫拓扑空间中的常见最佳临近点定理
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-07-09 DOI: 10.1186/s13660-024-03168-4
A. Sreelakshmi Unni, V. Pragadeeswarar
{"title":"Common best proximity point theorems in Hausdorff topological spaces","authors":"A. Sreelakshmi Unni, V. Pragadeeswarar","doi":"10.1186/s13660-024-03168-4","DOIUrl":"https://doi.org/10.1186/s13660-024-03168-4","url":null,"abstract":"In the present paper, we have obtained common best proximity point theorems of nonself maps in Hausdorff topological space. Further, our results extend the results due to Gerald F. Jungck, thereby proving a generalized version of Kirk’s theorem (J. London Math. 1(1):107–111, 1969).","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"80 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141568432","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}
引用次数: 0
Self-adaptive alternating direction method of multiplier for a fourth order variational inequality 四阶变分不等式的自适应交替方向乘法
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-07-09 DOI: 10.1186/s13660-024-03163-9
Jia Wu, Shougui Zhang
{"title":"Self-adaptive alternating direction method of multiplier for a fourth order variational inequality","authors":"Jia Wu, Shougui Zhang","doi":"10.1186/s13660-024-03163-9","DOIUrl":"https://doi.org/10.1186/s13660-024-03163-9","url":null,"abstract":"We propose an alternating direction method of multiplier for approximation solution of the unilateral obstacle problem with the biharmonic operator. We introduce an auxiliary unknown and augmented Lagrangian functional to deal with the inequality constrained, and we deduce a constrained minimization problem that is equivalent to a saddle-point problem. Then the alternating direction method of multiplier is applied to the corresponding problem. By using iterative functions, a self-adaptive rule is used to adjust the penalty parameter automatically. We show the convergence of the method and give the penalty parameter approximation in detail. Finally, the numerical results are given to illustrate the efficiency of the proposed method.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"22 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141568431","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}
引用次数: 0
Correction of nonmonotone trust region algorithm based on a modified diagonal regularized quasi-Newton method 基于修正对角正则化准牛顿法的非单调信任区域算法的修正
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-07-04 DOI: 10.1186/s13660-024-03161-x
Seyed Hamzeh Mirzaei, Ali Ashrafi
{"title":"Correction of nonmonotone trust region algorithm based on a modified diagonal regularized quasi-Newton method","authors":"Seyed Hamzeh Mirzaei, Ali Ashrafi","doi":"10.1186/s13660-024-03161-x","DOIUrl":"https://doi.org/10.1186/s13660-024-03161-x","url":null,"abstract":"In this paper, a new appropriate diagonal matrix estimation of the Hessian is introduced by minimizing the Byrd and Nocedal function subject to the weak secant equation. The Hessian estimate is used to correct the framework of a nonmonotone trust region algorithm with the regularized quasi-Newton method. Moreover, to counteract the adverse effect of monotonicity, we introduce a new nonmonotone strategy. The global and superlinear convergence of the suggested algorithm is established under some standard conditions. The numerical experiments on unconstrained optimization test functions show that the new algorithm is efficient and robust.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"2015 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141551266","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}
引用次数: 0
Upper bound for the second and third Hankel determinants of analytic functions associated with the error function and q-convolution combination 与误差函数和 q 卷积组合相关的解析函数的第二和第三汉克尔行列式的上限
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-07-04 DOI: 10.1186/s13660-024-03151-z
Hari M. Srivastava, Daniel Breaz, Alhanouf Alburaikan, Sheza M. El-Deeb
{"title":"Upper bound for the second and third Hankel determinants of analytic functions associated with the error function and q-convolution combination","authors":"Hari M. Srivastava, Daniel Breaz, Alhanouf Alburaikan, Sheza M. El-Deeb","doi":"10.1186/s13660-024-03151-z","DOIUrl":"https://doi.org/10.1186/s13660-024-03151-z","url":null,"abstract":"Recently, El-Deeb and Cotîrlă (Mathematics 11:11234834, 2023) used the error function together with a q-convolution to introduce a new operator. By means of this operator the following class $mathcal{R}_{alpha ,Upsilon}^{lambda ,q}(delta ,eta )$ of analytic functions was studied: $$begin{aligned} &mathcal{R}_{alpha ,Upsilon }^{lambda ,q}(delta ,eta ) &quad := biggl{ mathcal{ F}: {Re} biggl( (1-delta +2eta ) frac{mathcal{H}_{Upsilon }^{lambda ,q}mathcal{F}(zeta )}{zeta}+(delta -2eta ) bigl(mathcal{H} _{Upsilon}^{lambda ,q}mathcal{F}(zeta ) bigr) ^{{ prime}}+eta zeta bigl( mathcal{H}_{Upsilon}^{lambda ,q} mathcal{F}( zeta ) bigr) ^{{{prime prime}}} biggr) biggr} &quad >alpha quad (0leqq alpha < 1). end{aligned}$$ For these general analytic functions $mathcal{F}in mathcal{R}_{beta ,Upsilon}^{lambda ,q}(delta , eta )$ , we give upper bounds for the Fekete–Szegö functional and for the second and third Hankel determinants.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"101 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141551267","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}
引用次数: 0
Inertial iterative method for solving generalized equilibrium, variational inequality, and fixed point problems of multivalued mappings in Banach space 解决巴拿赫空间多值映射的广义均衡、变式不等式和定点问题的惯性迭代法
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-07-03 DOI: 10.1186/s13660-024-03166-6
Saud Fahad Aldosary, Mohammad Farid
{"title":"Inertial iterative method for solving generalized equilibrium, variational inequality, and fixed point problems of multivalued mappings in Banach space","authors":"Saud Fahad Aldosary, Mohammad Farid","doi":"10.1186/s13660-024-03166-6","DOIUrl":"https://doi.org/10.1186/s13660-024-03166-6","url":null,"abstract":"We devise an iterative algorithm incorporating inertial techniques to approximate the shared solution of a generalized equilibrium problem, a fixed point problem for a finite family of relatively nonexpansive multivalued mappings, and a variational inequality problem. Our discussion encompasses the strong convergence of the proposed algorithm and highlights specific outcomes derived from our theorem. Additionally, we provide a computational analysis to underscore the significance of our findings and draw comparisons. The results presented in this paper serve to extend and unify numerous previously established outcomes in this particular research domain.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"59 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141526892","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}
引用次数: 0
Asymptotic stability and bifurcations of a perturbed McMillan map 扰动麦克米兰图的渐近稳定性和分岔
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-07-02 DOI: 10.1186/s13660-024-03167-5
Lili Qian, Qiuying Lu, Guifeng Deng
{"title":"Asymptotic stability and bifurcations of a perturbed McMillan map","authors":"Lili Qian, Qiuying Lu, Guifeng Deng","doi":"10.1186/s13660-024-03167-5","DOIUrl":"https://doi.org/10.1186/s13660-024-03167-5","url":null,"abstract":"This paper presents various bifurcations of the McMillan map under perturbations of its coefficients, such as period-doubling, pitchfork, and hysteresis bifurcation. The associated existence regions are located. Using the quasi-Lyapunov function method, the existence of asymptotically stable fixed point is also demonstrated.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"67 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141532377","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}
引用次数: 0
Quasinormed spaces generated by a quasimodular 由准模块生成的准规范空间
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-06-28 DOI: 10.1186/s13660-024-03162-w
Paweł Foralewski, Henryk Hudzik, Paweł Kolwicz
{"title":"Quasinormed spaces generated by a quasimodular","authors":"Paweł Foralewski, Henryk Hudzik, Paweł Kolwicz","doi":"10.1186/s13660-024-03162-w","DOIUrl":"https://doi.org/10.1186/s13660-024-03162-w","url":null,"abstract":"In this paper, we introduce the notion of a quasimodular and we prove that the respective Minkowski functional of the unit quasimodular ball becomes a quasinorm. In this way, we refer to and complete the well-known theory related to the notions of a modular and a convex modular that lead to the F-norm and to the norm, respectively. We use the obtained results to consider the basic properties of quasinormed Calderón–Lozanovskiĭ spaces $E_{varphi}$ , where the lower Matuszewska–Orlicz index $alpha _{varphi}$ plays the key role. Our studies are conducted in a full possible generality.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"9 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141505933","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}
引用次数: 0
Approximation properties by shifted knots type of α-Bernstein–Kantorovich–Stancu operators α-Bernstein-Kantorovich-Stancu 算子的移结型逼近特性
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-06-27 DOI: 10.1186/s13660-024-03164-8
Md. Nasiruzzaman, Mohammad Dilshad, Bader Mufadhi Eid Albalawi, Mohammad Rehan Ajmal
{"title":"Approximation properties by shifted knots type of α-Bernstein–Kantorovich–Stancu operators","authors":"Md. Nasiruzzaman, Mohammad Dilshad, Bader Mufadhi Eid Albalawi, Mohammad Rehan Ajmal","doi":"10.1186/s13660-024-03164-8","DOIUrl":"https://doi.org/10.1186/s13660-024-03164-8","url":null,"abstract":"Through the real polynomials of the shifted knots, the α-Bernstein–Kantorovich operators are studied in their Stancu form, and the approximation properties are obtained. We obtain some direct approximation theorem in terms of Lipschitz type maximum function and Peetre’s K-functional, as well as Korovkin’s theorem. Eventually, the modulus of continuity is used to compute the upper bound error estimation.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"25 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141505934","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}
引用次数: 0
An inertial self-adaptive algorithm for solving split feasibility problems and fixed point problems in the class of demicontractive mappings 一种惯性自适应算法，用于解决去收缩映射类中的分割可行性问题和定点问题
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-06-11 DOI: 10.1186/s13660-024-03155-9
Vasile Berinde
{"title":"An inertial self-adaptive algorithm for solving split feasibility problems and fixed point problems in the class of demicontractive mappings","authors":"Vasile Berinde","doi":"10.1186/s13660-024-03155-9","DOIUrl":"https://doi.org/10.1186/s13660-024-03155-9","url":null,"abstract":"We propose a hybrid inertial self-adaptive algorithm for solving the split feasibility problem and fixed point problem in the class of demicontractive mappings. Our results are very general and extend several related results existing in the literature from the class of nonexpansive or quasi-nonexpansive mappings to the larger class of demicontractive mappings. Examples to illustrate numerically the effectiveness of the new analytical results are presented.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"154 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141505935","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}
引用次数: 0
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