Pub Date : 2024-09-09DOI: 10.1186/s13663-024-00770-5
Imo Kalu Agwu, Hüseyin Işık, Donatus Ikechi Igbokwe
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.
{"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}
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.
{"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}
Pub Date : 2024-04-01DOI: 10.1186/s13663-024-00763-4
Gopinath Janardhanan, Gunaseelan Mani, Edwin Antony Raj Michael, Sabri T. M. Thabet, Imed Kedim
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.
{"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}
Pub Date : 2024-03-18DOI: 10.1186/s13663-024-00762-5
Muhammad Sarwar, Syed Khayyam Shah, Kamaleldin Abodayeh, Arshad Khan, Ishak Altun
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.
{"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}
Pub Date : 2024-03-04DOI: 10.1186/s13663-024-00761-6
Bikramjit Acharjee, Guru Prem Prasad M
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.
{"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}
Pub Date : 2024-02-01DOI: 10.1186/s13663-023-00759-6
Menaha Dhanraj, Arul Joseph Gnanaprakasam, Santosh Kumar
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.
在本文中，我们提出了正交混合插值里奇-伊斯特斯特斯库斯型收缩图在正交 b 计量空间上的定点定理，以熟练地修改这一类。此外，我们还提供了一些例子来支持我们的主要结果。最后，我们提供了一个用数值结果求解积分方程的存在性和唯一性的应用，这在更大程度上是强大的。
{"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}
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.
本文阐述并证明了 S 多乘度量空间中的一些定点定理。本文还证明了各种 S 多乘度量空间的一些定点结果等同于 S 度量空间中的相应定点结果。本文列举了一些例子来验证我们主要结果的原创性和适用性。
{"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}
Pub Date : 2023-12-08DOI: 10.1186/s13663-023-00752-z
Solomon Gebregiorgis, Poom Kumam
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.
在本文中，我们证明了在希尔伯特空间环境中针对非展开映射的一般惯性曼-哈尔帕恩算法的强收敛定理。我们还证明了在希尔伯特空间环境中 k 严格伪收缩映射的一般惯性 Mann 算法的弱收敛定理。这些收敛结果扩展和概括了文献中的一些现有结果。最后，我们举例验证了我们的主要结果。
{"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}
Pub Date : 2023-11-27DOI: 10.1186/s13663-023-00754-x
Karim Chaira, Belkassem Seddoug
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.
设A和B是赋范空间X的两个非空子集，并设$T: A cup B 到A cup B$是一个循环(正则表达式)。(非循环)映射。本文的目的是在T上建立保证其相对非扩张性的弱条件。这个想法是为了恢复Matkowski (Banach J. Math)在两篇论文中提到的结果。植物学报，2007;[j] .不动点理论，24(7)，2022)，用一个循环(循环)代替非膨胀映射$f: C 到C$。(非循环)相对非扩展映射，以获得最佳邻近对。此外，我们还提供了一个函数方程的应用。
{"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}
Pub Date : 2023-11-20DOI: 10.1186/s13663-023-00755-w
Rafael Stekolshchik
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.
{"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}
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