scholarly journals Some New Results on a Three-Step Iteration Process

Axioms ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 110
Author(s):  
Kifayat Ullah ◽  
Junaid Ahmad ◽  
Manuel de la Sen
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Current Literature ◽  
Iterative Process ◽  
Research Work ◽  
Iteration Process ◽  
The Other ◽  
Weak And Strong Convergence ◽  
Convergence Results ◽  
Split Feasibility

The purpose of this research work is to prove some weak and strong convergence results for maps satisfying (E)-condition through three-step Thakur (J. Inequal. Appl.2014, 2014:328.) iterative process in Banach spaces. We also present a new example of maps satisfying (E)-condition, and prove that its three-step Thakur iterative process is more efficient than the other well-known three-step iterative processes. At the end of the paper, we apply our results for finding solutions of split feasibility problems. The presented research work updates some of the results of the current literature.

Some convergence results of M iterative process in Banach spaces

2019 ◽  
pp. 2150017 ◽  
Author(s):  
Kifayat Ullah ◽  
Faiza Ayaz ◽  
Junaid Ahmad
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Weak And Strong Convergence ◽  
Convergence Results

In this paper, we prove some weak and strong convergence results for generalized [Formula: see text]-nonexpansive mappings using [Formula: see text] iteration process in the framework of Banach spaces. This generalizes former results proved by Ullah and Arshad [Numerical reckoning fixed points for Suzuki’s generalized nonexpansive mappings via new iteration process, Filomat 32(1) (2018) 187–196].

scholarly journals On weak and strong convergence of an explicit iteration process for a total asymptotically quasi-I-nonexpansive mapping in Banach space

Filomat ◽  
2014 ◽  
Vol 28 (8) ◽  
pp. 1699-1710
Author(s):  
Hukmi Kiziltunc ◽  
Yunus Purtas
Keyword(s):  
Banach Space ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Iterative Process ◽  
Iteration Process ◽  
Nonempty Closed Convex Subset ◽  
Weak And Strong Convergence ◽  
New Class ◽  
Convergence Results ◽  
Definition Of

In this paper, we introduce a new class of Lipschitzian maps and prove some weak and strong convergence results for explicit iterative process using a more satisfactory definition of self mappings. Our results approximate common fixed point of a total asymptotically quasi-I-nonexpansive mapping T and a total asymptotically quasi-nonexpansive mapping I, defined on a nonempty closed convex subset of a Banach space.

scholarly journals Fixed-Point Convergence Results of a Three-Step Iterative Process in CAT(0) Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Kifayat Ullah ◽  
Junaid Ahmad ◽  
Muhammad Arshad ◽  
Manuel De la Sen
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Current Literature ◽  
Iterative Process ◽  
Iteration Process ◽  
Iterative Processes ◽  
Convergence Results ◽  
The Many

In this article, we suggest some Δ and strong convergence results of a three-step Sahu–Thakur iteration process for Garcia-Falset maps in the nonlinear setting of CAT(0) spaces. We furnish a new example of Garcia-Falset maps and prove that its three-step Sahu–Thakur iterative process is more effective than the many well-known iterative processes. Our results improve and extend some recently announced results of the current literature.

scholarly journals Hybrid Implicit Iteration Process for a Finite Family of Non-Self-Nonexpansive Mappings in Uniformly Convex Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Qiaohong Jiang ◽  
Jinghai Wang ◽  
Jianhua Huang
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Finite Family ◽  
Uniformly Convex ◽  
Weak And Strong Convergence ◽  
Convergence Theorems ◽  
Uniformly Convex Banach Spaces ◽  
Implicit Iteration

Weak and strong convergence theorems are established for hybrid implicit iteration for a finite family of non-self-nonexpansive mappings in uniformly convex Banach spaces. The results presented in this paper extend and improve some recent results.

scholarly journals Iterative Approximation of Endpoints for Multivalued Mappings in Banach Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-5 ◽  
Author(s):  
Thabet Abdeljawad ◽  
Kifayat Ullah ◽  
Junaid Ahmad ◽  
Nabil Mlaiki
Keyword(s):  
Banach Spaces ◽  
Fixed Point Theory ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Point Theory ◽  
Iterative Sequence ◽  
Multivalued Mappings ◽  
Weak And Strong Convergence ◽  
Iterative Approximation ◽  
Convergence Results

The purpose of this paper is to introduce the modified Agarwal-O’Regan-Sahu iteration process (S-iteration) for finding endpoints of multivalued nonexpansive mappings in the setting of Banach spaces. Under suitable conditions, some weak and strong convergence results of the iterative sequence generated by the proposed process are proved. Our results especially improve and unify some recent results of Panyanak (J. Fixed Point Theory Appl. (2018)). At the end of the paper, we offer an example to illustrate the main results.

scholarly journals Approximation of Fixed Points for Suzuki’s Generalized Non-Expansive Mappings

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 522 ◽  
Author(s):  
Javid Ali ◽  
Faeem Ali ◽  
Puneet Kumar
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Uniformly Convex ◽  
Weak And Strong Convergence ◽  
Numerical Example ◽  
Matlab Program ◽  
Convergence Results ◽  
Uniformly Convex Banach Spaces

In this paper, we study a three step iterative scheme to approximate fixed points of Suzuki’s generalized non-expansive mappings. We establish some weak and strong convergence results for such mappings in uniformly convex Banach spaces. Further, we show numerically that the considered iterative scheme converges faster than some other known iterations for Suzuki’s generalized non-expansive mappings. To support our claim, we give an illustrative numerical example and approximate fixed points of such mappings using Matlab program. Our results are new and generalize several relevant results in the literature.

scholarly journals Convergence of CR-iteration to common fixed points of three g-nonexpansive mappings in Banach spaces with graphs

2019 ◽  
Vol 16 (3) ◽  
pp. 76
Author(s):  
Nguyen Trung Hieu ◽  
Pham Thi Ngoc Mai
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Common Fixed Points ◽  
Weak And Strong Convergence ◽  
Numerical Example

The research introduces CR-iteration process and establishes some results about the weak and strong convergence of CR-iteration process to common fixed points of three G-nonexpansive mappings in uniformly convexBanach spaces with graphs. In addition, a numerical example is provided to illustrate for the convergence of CR-iteration process to common fixed points three G-nonexpansive mappings.

scholarly journals Approximation of Fixed Points for Suzuki's Generalized Non-Expansive Mappings

2019 ◽  
Author(s):  
Javid Ali ◽  
Faeem Ali ◽  
Puneet Kumar
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Uniformly Convex ◽  
Weak And Strong Convergence ◽  
Matlab Program ◽  
Convergence Results ◽  
Uniformly Convex Banach Spaces

In this paper, we study a three step iterative scheme to approximate fixed points of Suzuki's generalized non-expansive mappings. We establish some weak and strong convergence results for such mappings in uniformly convex Banach spaces. Further, we show numerically that iterative scheme (1.8) converges faster than some other known iterations for Suzuki's generalized non-expansive mappings. To support our claim, we give an illustrative example and approximate fixed points of such mappings using Matlab program. Our results are new and generalize several relevant results in the literature.

Inertial accelerated algorithms for solving split feasibility with multiple output sets in Hilbert spaces

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Chibueze C. Okeke ◽  
Lateef O. Jolaoso ◽  
Yekini Shehu
Keyword(s):  
Strong Convergence ◽  
Prior Knowledge ◽  
Hilbert Spaces ◽  
Split Feasibility Problem ◽  
Feasibility Problem ◽  
Weak And Strong Convergence ◽  
Numerical Examples ◽  
Mild Conditions ◽  
Convergence Results ◽  
Split Feasibility

Abstract In this paper, we propose two inertial accelerated algorithms which do not require prior knowledge of operator norm for solving split feasibility problem with multiple output sets in real Hilbert spaces. We prove weak and strong convergence results for approximating the solution of the considered problem under certain mild conditions. We also give some numerical examples to demonstrate the performance and efficiency of our proposed algorithms over some existing related algorithms in the literature.

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