Pub Date : 2021-03-08DOI: 10.1186/s13663-021-00692-6
Md. Asaduzzaman
In this paper, we introduce and study a modified multi-step Noor iterative procedure with errors for two Lipschitz strictly hemicontractive-type mappings in arbitrary Banach spaces and constitute its convergence and stability. The obtained results in this paper generalize and extend the corresponding result of Hussain et al. (Fixed Point Theory Appl. 2012:160, 2012) and some analogous results of several authors in the literature. Finally, a numerical example is included to illustrate our analytical results and to display the efficiency of our proposed novel iterative procedure with errors.
本文针对任意巴拿赫空间中的两个 Lipschitz 严格半收缩型映射，引入并研究了一个修正的多步 Noor 迭代过程（带误差），并构成了其收敛性和稳定性。本文得到的结果概括并扩展了 Hussain 等人（《定点理论应用》，2012:160，2012 年）的相应结果，以及文献中几位作者的一些类似结果。最后，本文还列举了一个数值示例来说明我们的分析结果，并展示了我们提出的新型误差迭代程序的效率。
{"title":"Convergence and stability of modified multi-step Noor iterative procedure with errors for strictly hemicontractive-type mappings in Banach spaces","authors":"Md. Asaduzzaman","doi":"10.1186/s13663-021-00692-6","DOIUrl":"https://doi.org/10.1186/s13663-021-00692-6","url":null,"abstract":"In this paper, we introduce and study a modified multi-step Noor iterative procedure with errors for two Lipschitz strictly hemicontractive-type mappings in arbitrary Banach spaces and constitute its convergence and stability. The obtained results in this paper generalize and extend the corresponding result of Hussain et al. (Fixed Point Theory Appl. 2012:160, 2012) and some analogous results of several authors in the literature. Finally, a numerical example is included to illustrate our analytical results and to display the efficiency of our proposed novel iterative procedure with errors.","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140885750","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-02-22DOI: 10.1186/s13663-021-00689-1
Konrawut Khammahawong, Poom Kumam, Parin Chaipunya, Somyot Plubtieng
We propose Tseng’s extragradient methods for finding a solution of variational inequality problems associated with pseudomonotone vector fields in Hadamard manifolds. Under standard assumptions such as pseudomonotone and Lipschitz continuous vector fields, we prove that any sequence generated by the proposed methods converges to a solution of variational inequality problem, whenever it exits. Moreover, we give some numerical experiments to illustrate our main results.
{"title":"New Tseng’s extragradient methods for pseudomonotone variational inequality problems in Hadamard manifolds","authors":"Konrawut Khammahawong, Poom Kumam, Parin Chaipunya, Somyot Plubtieng","doi":"10.1186/s13663-021-00689-1","DOIUrl":"https://doi.org/10.1186/s13663-021-00689-1","url":null,"abstract":"We propose Tseng’s extragradient methods for finding a solution of variational inequality problems associated with pseudomonotone vector fields in Hadamard manifolds. Under standard assumptions such as pseudomonotone and Lipschitz continuous vector fields, we prove that any sequence generated by the proposed methods converges to a solution of variational inequality problem, whenever it exits. Moreover, we give some numerical experiments to illustrate our main results.","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140885757","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we investigate the existence and the uniqueness of a common fixed point of a pair of self-mappings satisfying new contractive type conditions on a modular metric space endowed with a reflexive digraph. An application is given to show the use of our main result.
{"title":"Common fixed point for some generalized contractive mappings in a modular metric space with a graph","authors":"Karim Chaira, Abderrahim Eladraoui, Mustapha Kabil, Abdessamad Kamouss","doi":"10.1186/s13663-021-00690-8","DOIUrl":"https://doi.org/10.1186/s13663-021-00690-8","url":null,"abstract":"In this paper, we investigate the existence and the uniqueness of a common fixed point of a pair of self-mappings satisfying new contractive type conditions on a modular metric space endowed with a reflexive digraph. An application is given to show the use of our main result.","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140885754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-25DOI: 10.1186/s13663-021-00688-2
Zhiqun Xue, Guiwen Lv
In this paper, we obtain a new convergence theorem for fixed points of weak contractions in Branciari type generalized metric spaces under weaker conditions. The proof process of the theorem is new and different from that of other authors. An illustrative example of this theorem is to show how the new conditions extend known results.
{"title":"A fixed point theorem for generalized ((psi ,varphi ))-weak contractions in Branciari type generalized metric spaces","authors":"Zhiqun Xue, Guiwen Lv","doi":"10.1186/s13663-021-00688-2","DOIUrl":"https://doi.org/10.1186/s13663-021-00688-2","url":null,"abstract":"In this paper, we obtain a new convergence theorem for fixed points of weak contractions in Branciari type generalized metric spaces under weaker conditions. The proof process of the theorem is new and different from that of other authors. An illustrative example of this theorem is to show how the new conditions extend known results.","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"2013 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140885892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-01DOI: 10.1186/s13663-020-00686-w
Yuanheng Wang, Xiuping Wu, Chanjuan Pan
{"title":"The iterative solutions of split common fixed point problem for asymptotically nonexpansive mappings in Banach spaces","authors":"Yuanheng Wang, Xiuping Wu, Chanjuan Pan","doi":"10.1186/s13663-020-00686-w","DOIUrl":"https://doi.org/10.1186/s13663-020-00686-w","url":null,"abstract":"","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"2020 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13663-020-00686-w","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"65789539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-09DOI: 10.1186/s13663-020-00684-y
Noureddine El Harmouchi, Karim Chaira, El Miloudi Marhrani
In this paper, we consider the class of monotone ρ-nonexpansive semigroups and give existence and convergence results for common fixed points. First, we prove that the set of common fixed points is nonempty in uniformly convex modular spaces and modular spaces. Then we introduce an iteration algorithm to approximate a common fixed point for the same class of semigroups.
{"title":"Common fixed points of monotone ρ-nonexpansive semigroup in modular spaces","authors":"Noureddine El Harmouchi, Karim Chaira, El Miloudi Marhrani","doi":"10.1186/s13663-020-00684-y","DOIUrl":"https://doi.org/10.1186/s13663-020-00684-y","url":null,"abstract":"In this paper, we consider the class of monotone ρ-nonexpansive semigroups and give existence and convergence results for common fixed points. First, we prove that the set of common fixed points is nonempty in uniformly convex modular spaces and modular spaces. Then we introduce an iteration algorithm to approximate a common fixed point for the same class of semigroups.","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140885755","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-02DOI: 10.1186/s13663-020-00683-z
Joy C. Umudu, Johnson O. Olaleru, Adesanmi A. Mogbademu
In this paper, fixed point results for a newly introduced Geraghty quasi-contraction type mappings are proved in more general metric spaces called T-orbitally complete dislocated quasi-metric spaces. Geraghty quasi-contraction type mappings generalize, among others, Ciric’s quasi-contraction mappings and other Geraghty quasi-contractive type mappings in the literature. Fixed point results are obtained without imposing a continuity condition on the mapping, thereby further generalizing some other related work in the literature. An example is given to show the validity of results obtained.
{"title":"Fixed point results for Geraghty quasi-contraction type mappings in dislocated quasi-metric spaces","authors":"Joy C. Umudu, Johnson O. Olaleru, Adesanmi A. Mogbademu","doi":"10.1186/s13663-020-00683-z","DOIUrl":"https://doi.org/10.1186/s13663-020-00683-z","url":null,"abstract":"In this paper, fixed point results for a newly introduced Geraghty quasi-contraction type mappings are proved in more general metric spaces called T-orbitally complete dislocated quasi-metric spaces. Geraghty quasi-contraction type mappings generalize, among others, Ciric’s quasi-contraction mappings and other Geraghty quasi-contractive type mappings in the literature. Fixed point results are obtained without imposing a continuity condition on the mapping, thereby further generalizing some other related work in the literature. An example is given to show the validity of results obtained.","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"47 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140885970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-01DOI: 10.1186/s13663-020-00682-0
Hayel N. Saleh, Mohammad Imdad, Md Hasanuzzaman
In the present paper, we adopt a short and sharpened approach to prove fixed point results involving fuzzy $mathcal{H}$ -contractive mappings utilized in (Wardowski, Fuzzy Sets Syst. 125:245–252, 2013) and other related articles. In this process, we are able to relax some conditions utilized by earlier authors which in turn yields affirmative answers to some open questions raised by earlier authors.
{"title":"A short and sharpened way to approach fixed point results involving fuzzy (mathcal{H})-contractive mappings","authors":"Hayel N. Saleh, Mohammad Imdad, Md Hasanuzzaman","doi":"10.1186/s13663-020-00682-0","DOIUrl":"https://doi.org/10.1186/s13663-020-00682-0","url":null,"abstract":"In the present paper, we adopt a short and sharpened approach to prove fixed point results involving fuzzy $mathcal{H}$\u0000-contractive mappings utilized in (Wardowski, Fuzzy Sets Syst. 125:245–252, 2013) and other related articles. In this process, we are able to relax some conditions utilized by earlier authors which in turn yields affirmative answers to some open questions raised by earlier authors.","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140885569","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-22DOI: 10.1186/s13663-020-00681-1
Frank H. Page, Jing Fu
{"title":"K-Correspondences, USCOs, and fixed point problems arising in discounted stochastic games","authors":"Frank H. Page, Jing Fu","doi":"10.1186/s13663-020-00681-1","DOIUrl":"https://doi.org/10.1186/s13663-020-00681-1","url":null,"abstract":"","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"2020 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13663-020-00681-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"65789525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-08-21DOI: 10.1186/s13663-020-00680-2
C. E. Chidume, A. Adamu, M. O. Nnakwe
An inertial iterative algorithm is proposed for approximating a solution of a maximal monotone inclusion in a uniformly convex and uniformly smooth real Banach space. The sequence generated by the algorithm is proved to converge strongly to a solution of the inclusion. Moreover, the theorem proved is applied to approximate a solution of a convex optimization problem and a solution of a Hammerstein equation. Furthermore, numerical experiments are given to compare, in terms of CPU time and number of iterations, the performance of the sequence generated by our algorithm with the performance of the sequences generated by three recent inertial type algorithms for approximating zeros of maximal monotone operators. In addition, the performance of the sequence generated by our algorithm is compared with the performance of a sequence generated by another recent algorithm for approximating a solution of a Hammerstein equation. Finally, a numerical example is given to illustrate the implementability of our algorithm for approximating a solution of a convex optimization problem.
本文提出了一种惯性迭代算法，用于逼近均匀凸均匀光滑实Banach空间中最大单调包含的解。该算法生成的序列被证明强收敛于该包含的解。此外，所证明的定理还被应用于近似凸优化问题的解和哈默斯坦方程的解。此外，我们还给出了数值实验，从 CPU 时间和迭代次数的角度，比较了我们的算法生成的序列与最近三种惯性型算法生成的序列在近似最大单调算子零点方面的性能。此外，我们还将算法生成序列的性能与另一种最新算法生成序列的性能进行了比较，后者用于逼近哈默斯坦方程的解。最后，我们给出了一个数值示例，以说明我们的算法在近似凸优化问题解时的可实施性。
{"title":"Strong convergence of an inertial algorithm for maximal monotone inclusions with applications","authors":"C. E. Chidume, A. Adamu, M. O. Nnakwe","doi":"10.1186/s13663-020-00680-2","DOIUrl":"https://doi.org/10.1186/s13663-020-00680-2","url":null,"abstract":"An inertial iterative algorithm is proposed for approximating a solution of a maximal monotone inclusion in a uniformly convex and uniformly smooth real Banach space. The sequence generated by the algorithm is proved to converge strongly to a solution of the inclusion. Moreover, the theorem proved is applied to approximate a solution of a convex optimization problem and a solution of a Hammerstein equation. Furthermore, numerical experiments are given to compare, in terms of CPU time and number of iterations, the performance of the sequence generated by our algorithm with the performance of the sequences generated by three recent inertial type algorithms for approximating zeros of maximal monotone operators. In addition, the performance of the sequence generated by our algorithm is compared with the performance of a sequence generated by another recent algorithm for approximating a solution of a Hammerstein equation. Finally, a numerical example is given to illustrate the implementability of our algorithm for approximating a solution of a convex optimization problem.","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"110 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140886069","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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