Weak and strong convergence results for solving inclusion problems and its applications

2021 ◽  
Author(s):  
Jun Yang ◽  
Huali Zhao ◽  
Min An
Keyword(s):  
Strong Convergence ◽  
Weak And Strong Convergence ◽  
Inclusion Problems ◽  
Convergence Results

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].

Modified inertial subgradient extragradient method for equilibrium problems

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Lateef Olakunle Jolaoso ◽  
Yekini Shehu ◽  
Regina N. Nwokoye
Keyword(s):  
Variational Inequalities ◽  
Strong Convergence ◽  
Equilibrium Problems ◽  
Extragradient Method ◽  
Subgradient Extragradient Method ◽  
Weak And Strong Convergence ◽  
Extragradient Methods ◽  
Convergence Results ◽  
Inertial Extrapolation ◽  
Special Case

Abstract The subgradient extragradient method with inertial extrapolation step x n + θ n (x n − x n−1) (also known as inertial subgradient extragradient method) has been studied extensively in the literature for solving variational inequalities and equilibrium problems. Most of the inertial subgradient extragradient methods in the literature for both variational inequalities and equilibrium problems have not considered the special case when the inertial factor θ n = 1. The convergence results have always been obtained when the inertial factor θ n is assumed 0 ≤ θ n < 1. This paper considers the relaxed inertial version of subgradient extragradient method for equilibrium problems with 0 ≤ θ n ≤ 1. We give both weak and strong convergence results using this inertial subgradient extragradient method and also give some numerical illustrations.

scholarly journals Common Fixed Points for Weak and Strong Convergence Results

2016 ◽  
Vol 4 (2) ◽  
pp. 340
Author(s):  
S. C. Shrivastava
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Fixed Points ◽  
Iterative Scheme ◽  
Common Fixed Points ◽  
Convex Banach Space ◽  
Uniformly Convex Banach Space ◽  
Uniformly Convex ◽  
Weak And Strong Convergence ◽  
Convergence Results

<div><p> <em>In this paper, we study the approximation of common fixed points for more general classes of mappings through weak and strong convergence results of an iterative scheme in a uniformly convex Banach space. Our results extend and improve some known recent results.</em></p></div>

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 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 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.

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.

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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