Pub Date : 2024-07-11DOI: 10.1186/s13660-024-03169-3
Babar Sultan, Mehvish Sultan, Aziz Khan, Thabet Abdeljawad
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 ${dot{K} ^{alpha (cdot ), q),theta}_{ p(cdot )}(mathbb{R}^{n})}$ .
{"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}
Pub Date : 2024-07-09DOI: 10.1186/s13660-024-03168-4
A. Sreelakshmi Unni, V. Pragadeeswarar
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).
在本文中，我们获得了豪斯多夫拓扑空间中非自映射的共同最佳邻近点定理。此外，我们的结果扩展了杰拉尔德-F-容克（Gerald F. Jungck）的结果，从而证明了柯克定理（J. London Math.1(1):107-111, 1969).
{"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}
Pub Date : 2024-07-09DOI: 10.1186/s13660-024-03163-9
Jia Wu, Shougui Zhang
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.
{"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}
Pub Date : 2024-07-04DOI: 10.1186/s13660-024-03161-x
Seyed Hamzeh Mirzaei, Ali Ashrafi
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.
{"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}
Pub Date : 2024-07-04DOI: 10.1186/s13660-024-03151-z
Hari M. Srivastava, Daniel Breaz, Alhanouf Alburaikan, Sheza M. El-Deeb
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.
{"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}
Pub Date : 2024-07-03DOI: 10.1186/s13660-024-03166-6
Saud Fahad Aldosary, Mohammad Farid
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.
{"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}
Pub Date : 2024-07-02DOI: 10.1186/s13660-024-03167-5
Lili Qian, Qiuying Lu, Guifeng Deng
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.
{"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}
Pub Date : 2024-06-28DOI: 10.1186/s13660-024-03162-w
Paweł Foralewski, Henryk Hudzik, Paweł Kolwicz
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.
在本文中，我们引入了准模态的概念，并证明了单位准模态球的相应闵科夫斯基函数成为准规范。这样，我们参考并完成了与模数和凸模数概念相关的著名理论，这两个概念分别导致了 F 准则和规范。我们利用得到的结果来考虑准规范的卡尔德隆-洛扎诺夫斯基空间 $E_{varphi}$ 的基本性质，其中下马图谢夫斯基-奥利奇指数 $alpha _{varphi}$ 起着关键作用。我们的研究尽可能全面。
{"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}
Pub Date : 2024-06-27DOI: 10.1186/s13660-024-03164-8
Md. Nasiruzzaman, Mohammad Dilshad, Bader Mufadhi Eid Albalawi, Mohammad Rehan Ajmal
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.
{"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}
Pub Date : 2024-06-11DOI: 10.1186/s13660-024-03155-9
Vasile Berinde
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.
{"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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：