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Keywords = opial condition

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14 pages, 1219 KiB  
Article
Approximating Fixed Points of Nonexpansive Type Mappings via General Picard–Mann Algorithm
by Rahul Shukla and Rekha Panicker
Computation 2022, 10(9), 151; https://doi.org/10.3390/computation10090151 - 31 Aug 2022
Cited by 5 | Viewed by 2226
Abstract
The aim of this paper is to approximate fixed points of nonexpansive type mappings in Banach spaces when the set of fixed points is nonempty. We study the general Picard–Mann (GPM) algorithm, obtaining the weak and strong convergence theorems. We provide an example [...] Read more.
The aim of this paper is to approximate fixed points of nonexpansive type mappings in Banach spaces when the set of fixed points is nonempty. We study the general Picard–Mann (GPM) algorithm, obtaining the weak and strong convergence theorems. We provide an example to illustrate the convergence behaviour of the GPM algorithm. We compare the GPM algorithm with other existing (well known) algorithms numerically (under different parameters and initial guesses). Full article
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10 pages, 284 KiB  
Article
Some Iterative Approximation Results of F Iteration Process in Banach Spaces
by Junaid Ahmad, Kifayat Ullah, Imtiaz Ahmad, Muhammad Arshad, Nantapat Jarasthitikulchai and Weerawat Sudsutad
Axioms 2022, 11(4), 153; https://doi.org/10.3390/axioms11040153 - 25 Mar 2022
Cited by 1 | Viewed by 2304
Abstract
In this research, we suggest some convergence results for operators having (RCSC) condition in Banach space setting under F iterative scheme. We establish weak convergence under Opials condition and also establish some important strong convergence results under some [...] Read more.
In this research, we suggest some convergence results for operators having (RCSC) condition in Banach space setting under F iterative scheme. We establish weak convergence under Opials condition and also establish some important strong convergence results under some appropriate assumptions on the domain or on the mapping. We furnish a non-trivial example of mappings having (RCSC) condition and show that its F iterative scheme is more effective than the corresponding well known iterative schemes on this particular example. Full article
(This article belongs to the Special Issue Theory and Application of Fixed Point)
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10 pages, 279 KiB  
Article
Fixed Point Theorems for Nonexpansive Mappings under Binary Relations
by Aftab Alam, Reny George, Mohammad Imdad and Md Hasanuzzaman
Mathematics 2021, 9(17), 2059; https://doi.org/10.3390/math9172059 - 26 Aug 2021
Cited by 10 | Viewed by 2265
Abstract
In the present article, we establish relation-theoretic fixed point theorems in a Banach space, satisfying the Opial condition, using the R-Krasnoselskii sequence. We observe that graphical versions (Fixed Point Theory Appl. 2015:49 (2015) 6 pp.) and order-theoretic versions (Fixed Point Theory Appl. [...] Read more.
In the present article, we establish relation-theoretic fixed point theorems in a Banach space, satisfying the Opial condition, using the R-Krasnoselskii sequence. We observe that graphical versions (Fixed Point Theory Appl. 2015:49 (2015) 6 pp.) and order-theoretic versions (Fixed Point Theory Appl. 2015:110 (2015) 7 pp.) of such results can be extended to a transitive binary relation. Full article
16 pages, 269 KiB  
Article
On Iteration Sn for Operators with Condition (D)
by Cristian Ciobanescu and Teodor Turcanu
Symmetry 2020, 12(10), 1676; https://doi.org/10.3390/sym12101676 - 14 Oct 2020
Cited by 5 | Viewed by 1682
Abstract
A recently introduced nonexpansive-type condition is subjected to an in-depth analysis. New examples are provided to highlight the relationship with Suzuki-type mappings. Furthermore, a convergence survey is conducted based on the iteration procedure Sn. Issues related to data dependence and the [...] Read more.
A recently introduced nonexpansive-type condition is subjected to an in-depth analysis. New examples are provided to highlight the relationship with Suzuki-type mappings. Furthermore, a convergence survey is conducted based on the iteration procedure Sn. Issues related to data dependence and the stability of this iterative process are also being studied. Our study is performed in the framework of Banach spaces, in which the symmetry of the associated metric is a fundamental axiom and plays a key role while proving many results of this paper. Full article
(This article belongs to the Special Issue Numerical Algorithms for Fixed Point Problems and Applications)
10 pages, 272 KiB  
Article
Fibonacci–Mann Iteration for Monotone Asymptotically Nonexpansive Mappings in Modular Spaces
by Buthinah A. Bin Dehaish and Mohamed A Khamsi
Symmetry 2018, 10(10), 481; https://doi.org/10.3390/sym10100481 - 11 Oct 2018
Cited by 3 | Viewed by 3252
Abstract
In this work, we extend the fundamental results of Schu to the class of monotone asymptotically nonexpansive mappings in modular function spaces. In particular, we study the behavior of the Fibonacci–Mann iteration process, introduced recently by Alfuraidan and Khamsi, defined by [...] Read more.
In this work, we extend the fundamental results of Schu to the class of monotone asymptotically nonexpansive mappings in modular function spaces. In particular, we study the behavior of the Fibonacci–Mann iteration process, introduced recently by Alfuraidan and Khamsi, defined by x n + 1 = t n T ϕ ( n ) ( x n ) + ( 1 t n ) x n , for n N , when T is a monotone asymptotically nonexpansive self-mapping. Full article
(This article belongs to the Special Issue Fixed Point Theory and Fractional Calculus with Applications)
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