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Fixed Point Theory and Applications最新文献

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Weak and strong convergence theorems for a new class of enriched strictly pseudononspreading mappings in Hilbert spaces 希尔伯特空间中一类新的富集严格伪展开映射的弱收敛定理和强收敛定理
Fixed Point Theory and Applications Pub Date : 2024-09-09 DOI: 10.1186/s13663-024-00770-5
Imo Kalu Agwu, Hüseyin Işık, Donatus Ikechi Igbokwe
{"title":"Weak and strong convergence theorems for a new class of enriched strictly pseudononspreading mappings in Hilbert spaces","authors":"Imo Kalu Agwu, Hüseyin Işık, Donatus Ikechi Igbokwe","doi":"10.1186/s13663-024-00770-5","DOIUrl":"https://doi.org/10.1186/s13663-024-00770-5","url":null,"abstract":"Let Ω be a nonempty closed convex subset of a real Hilbert space $mathfrak{H}$ . Let ℑ be a nonspreading mapping from Ω into itself. Define two sequences ${psi _{{n}}}_{n=1}^{infty}$ and ${phi _{{n}}}_{n=1}^{infty}$ as follows: $$begin{aligned} textstylebegin{cases} psi _{n+1}=pi _{n}psi _{{n}}+(1-pi _{n})Im psi _{{n}}, phi _{{n}}=dfrac{1}{n}underset{t=1}{overset{n}{sum}}psi _{t}, end{cases}displaystyle end{aligned}$$ for $nin mathit{N}$ , where $0leq pi _{n}leq 1$ , and $pi _{n} rightarrow 0$ . In 2010, Kurokawa and Takahashi established weak and strong convergence theorems of the sequences developed from the above Baillion-type iteration method (Nonlinear Anal. 73:1562–1568, 2010). In this paper, we prove weak and strong convergence theorems for a new class of $(eta ,beta )$ -enriched strictly pseudononspreading ( $(eta ,beta )$ -ESPN) maps, more general than that studied by Kurokawa and W. Takahashi in the setup of real Hilbert spaces. Further, by means of a robust auxiliary map incorporated in our theorems, the strong convergence of the sequence generated by Halpern-type iterative algorithm is proved thereby resolving in the affirmative the open problem raised by Kurokawa and Takahashi in their concluding remark for the case in which the map ℑ is averaged. Some nontrivial examples are given, and the results obtained extend, improve, and generalize several well-known results in the current literature.","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"56 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142180333","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}
引用次数: 0
Ϝ-Contraction of Hardy–Rogers type in supermetric spaces with applications 超对称空间中哈迪-罗杰斯类型的Ϝ-收缩及其应用
Fixed Point Theory and Applications Pub Date : 2024-07-08 DOI: 10.1186/s13663-024-00767-0
Kamaleldin Abodayeh, Syed Khayyam Shah, Muhammad Sarwar, Varaporn Wattanakejorn, Thanin Sitthiwirattham
{"title":"Ϝ-Contraction of Hardy–Rogers type in supermetric spaces with applications","authors":"Kamaleldin Abodayeh, Syed Khayyam Shah, Muhammad Sarwar, Varaporn Wattanakejorn, Thanin Sitthiwirattham","doi":"10.1186/s13663-024-00767-0","DOIUrl":"https://doi.org/10.1186/s13663-024-00767-0","url":null,"abstract":"This article focuses on studying some fixed-point results via Ϝ-contraction of Hardy–Rogers type in the context of supermetric space and ordered supermetric space. We also introduced rational-type z-contraction on supermetric space. For authenticity, some illustrative examples and applications have been included.","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141574801","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}
引用次数: 0
Solution of a nonlinear fractional-order initial value problem via a (mathscr{C}^{*})-algebra-valued (mathcal{R})-metric space 通过（(mathscr{C}^{*}）-代数值的（(mathcal{R}）-度量空间求解非线性分数阶初值问题
Fixed Point Theory and Applications Pub Date : 2024-04-01 DOI: 10.1186/s13663-024-00763-4
Gopinath Janardhanan, Gunaseelan Mani, Edwin Antony Raj Michael, Sabri T. M. Thabet, Imed Kedim
{"title":"Solution of a nonlinear fractional-order initial value problem via a (mathscr{C}^{*})-algebra-valued (mathcal{R})-metric space","authors":"Gopinath Janardhanan, Gunaseelan Mani, Edwin Antony Raj Michael, Sabri T. M. Thabet, Imed Kedim","doi":"10.1186/s13663-024-00763-4","DOIUrl":"https://doi.org/10.1186/s13663-024-00763-4","url":null,"abstract":"In this article, we prove new common fixed-point theorems on a $mathscr{C}^{*}$ -algebra-valued $mathcal{R}$ -metric space. An example is given based on our obtained results. To enhance our results, a strong application based on the fractional-order initial value problem is provided.","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140581645","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}
引用次数: 0
On a new generalization of a Perov-type F-contraction with application to a semilinear operator system 论 Perov 型 F-contraction 的新广义化及其在半线性算子系统中的应用
Fixed Point Theory and Applications Pub Date : 2024-03-18 DOI: 10.1186/s13663-024-00762-5
Muhammad Sarwar, Syed Khayyam Shah, Kamaleldin Abodayeh, Arshad Khan, Ishak Altun
{"title":"On a new generalization of a Perov-type F-contraction with application to a semilinear operator system","authors":"Muhammad Sarwar, Syed Khayyam Shah, Kamaleldin Abodayeh, Arshad Khan, Ishak Altun","doi":"10.1186/s13663-024-00762-5","DOIUrl":"https://doi.org/10.1186/s13663-024-00762-5","url":null,"abstract":"This manuscript aims to present new results about the generalized F-contraction of Hardy–Rogers-type mappings in a complete vector-valued metric space, and to demonstrate the fixed-point theorems for single and pairs of generalized F-contractions of Hardy–Rogers-type mappings. The established results represent a significant development of numerous previously published findings and results in the existing body of literature. Furthermore, to ensure the practicality and effectiveness of our findings across other fields, we provide an application that demonstrates a unique solution for the semilinear operator system within the Banach space.","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140155506","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}
引用次数: 0
Fixed point theorem and iterated function system in φ-metric modular space φ-度量模块空间中的定点定理和迭代函数系统
Fixed Point Theory and Applications Pub Date : 2024-03-04 DOI: 10.1186/s13663-024-00761-6
Bikramjit Acharjee, Guru Prem Prasad M
{"title":"Fixed point theorem and iterated function system in φ-metric modular space","authors":"Bikramjit Acharjee, Guru Prem Prasad M","doi":"10.1186/s13663-024-00761-6","DOIUrl":"https://doi.org/10.1186/s13663-024-00761-6","url":null,"abstract":"We introduce and study the concept of φ-metric modular space and, then define φ-α-Meir-Keeler contraction on it and explore its fixed point. Further, we define the Hausdorff distance between two non-empty compact subsets of the considered space. Some topological properties of φ-metric modular space are also explored. Additionally, we prove the existence of the attractor (fractal) of the IFS consisting of φ-α-Meir-Keeler contractions.","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025292","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}
引用次数: 0
Solving integral equations via orthogonal hybrid interpolative RI-type contractions 通过正交混合插值 RI 型收缩求解积分方程
Fixed Point Theory and Applications Pub Date : 2024-02-01 DOI: 10.1186/s13663-023-00759-6
Menaha Dhanraj, Arul Joseph Gnanaprakasam, Santosh Kumar
{"title":"Solving integral equations via orthogonal hybrid interpolative RI-type contractions","authors":"Menaha Dhanraj, Arul Joseph Gnanaprakasam, Santosh Kumar","doi":"10.1186/s13663-023-00759-6","DOIUrl":"https://doi.org/10.1186/s13663-023-00759-6","url":null,"abstract":"In this paper, we initiate the fixed point theorems for an orthogonal hybrid interpolative Riech Istrastescus type contractions map on orthogonal b-metric spaces to modify this class proficiently. Also, we provide some examples supporting our main results. Finally, we provide an application to solve the existence and uniqueness of an integral equation with numeric results, which is powerful in a greater way.","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139659239","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}
引用次数: 0
Equivalence of some results and fixed-point theorems in S-multiplicative metric spaces S-乘法度量空间中一些结果和定点定理的等价性
Fixed Point Theory and Applications Pub Date : 2024-01-03 DOI: 10.1186/s13663-023-00756-9
Olusola Kayode Adewale, Samuel Olusola Ayodele, Babatunde Eriwa Oyelade, Emmanuella Ehui Aribike
{"title":"Equivalence of some results and fixed-point theorems in S-multiplicative metric spaces","authors":"Olusola Kayode Adewale, Samuel Olusola Ayodele, Babatunde Eriwa Oyelade, Emmanuella Ehui Aribike","doi":"10.1186/s13663-023-00756-9","DOIUrl":"https://doi.org/10.1186/s13663-023-00756-9","url":null,"abstract":"In this paper, some fixed-point theorems are stated and proved in S-multiplicative metric spaces. We also show in this paper that some fixed-point results for various S-multiplicative metric spaces are equivalent to those of corresponding fixed-point results in S-metric spaces. Some examples are presented to validate the originality and applicability of our main results.","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139084191","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}
引用次数: 0
Convergence results on the general inertial Mann–Halpern and general inertial Mann algorithms 一般惯性曼-哈尔彭算法和一般惯性曼算法的收敛结果
Fixed Point Theory and Applications Pub Date : 2023-12-08 DOI: 10.1186/s13663-023-00752-z
Solomon Gebregiorgis, Poom Kumam
{"title":"Convergence results on the general inertial Mann–Halpern and general inertial Mann algorithms","authors":"Solomon Gebregiorgis, Poom Kumam","doi":"10.1186/s13663-023-00752-z","DOIUrl":"https://doi.org/10.1186/s13663-023-00752-z","url":null,"abstract":"In this paper, we prove strong convergence theorem of the general inertial Mann–Halpern algorithm for nonexpansive mappings in the setting of Hilbert spaces. We also prove weak convergence theorem of the general inertial Mann algorithm for k-strict pseudo-contractive mappings in the setting of Hilbert spaces. These convergence results extend and generalize some existing results in the literature. Finally, we provide examples to verify our main results.","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"149 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138560691","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}
引用次数: 0
On a generalization of a relatively nonexpansive mapping and best proximity pair 关于相对非扩张映射和最佳邻近对的推广
Fixed Point Theory and Applications Pub Date : 2023-11-27 DOI: 10.1186/s13663-023-00754-x
Karim Chaira, Belkassem Seddoug
{"title":"On a generalization of a relatively nonexpansive mapping and best proximity pair","authors":"Karim Chaira, Belkassem Seddoug","doi":"10.1186/s13663-023-00754-x","DOIUrl":"https://doi.org/10.1186/s13663-023-00754-x","url":null,"abstract":"Let A and B be two nonempty subsets of a normed space X, and let $T: A cup B to A cup B$ be a cyclic (resp., noncyclic) mapping. The objective of this paper is to establish weak conditions on T that ensure its relative nonexpansiveness. The idea is to recover the results mentioned in two papers by Matkowski (Banach J. Math. Anal. 2:237–244, 2007; J. Fixed Point Theory Appl. 24:70, 2022), by replacing the nonexpansive mapping $f: C to C$ with a cyclic (resp., noncyclic) relatively nonexpansive mapping to obtain the best proximity pair. Additionally, we provide an application to a functional equation.","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"91 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138507397","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}
引用次数: 0
Extending Snow’s algorithm for computations in the finite Weyl groups 扩展Snow算法在有限Weyl群中的计算
Fixed Point Theory and Applications Pub Date : 2023-11-20 DOI: 10.1186/s13663-023-00755-w
Rafael Stekolshchik
{"title":"Extending Snow’s algorithm for computations in the finite Weyl groups","authors":"Rafael Stekolshchik","doi":"10.1186/s13663-023-00755-w","DOIUrl":"https://doi.org/10.1186/s13663-023-00755-w","url":null,"abstract":"In 1990, D. Snow proposed an effective algorithm for computing the orbits of finite Weyl groups. Snow’s algorithm is designed for computation of weights, W-orbits, and elements of the Weyl group. An extension of Snow’s algorithm is proposed, which allows to find pairs of mutually inverse elements together with the calculation of W-orbits in the same runtime cycle. This simplifies the calculation of conjugacy classes in the Weyl group. As an example, the complete list of elements of the Weyl group $W(D_{4})$ obtained using the extended Snow’s algorithm. The elements of $W(D_{4})$ are specified in two ways: as reduced expressions and as matrices of the faithful representation. Then we give a partition of this group into conjugacy classes with elements specified as reduced expressions. Various forms are given for representatives of the conjugacy classes of $W(D_{4})$ : with Carter diagrams, with reduced expressions, and with signed cycle-types. In the Appendix, we provide an implementation of the algorithm in Python.","PeriodicalId":12293,"journal":{"name":"Fixed Point Theory and Applications","volume":"81 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138507398","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}
引用次数: 1
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