scholarly journals Weak and strong convergence of an explicit iteration process for an asymptotically quasi-i-nonexpansive mapping in Banach spaces

2012 ◽  
Vol 05 (05) ◽  
pp. 403-411 ◽  
Author(s):  
Yunus Purtas ◽  
Hukmi Kiziltunc
Keyword(s):  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Iteration Process ◽  
Weak And Strong Convergence

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 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 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 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 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.

scholarly journals On Reich type λ−α-nonexpansive mapping in Banach spaces with applications to L1([0,1])

2018 ◽  
Vol 19 (2) ◽  
pp. 291
Author(s):  
Rabah Belbaki ◽  
E. Karapinar ◽  
Amar Ould-Hammouda,
Keyword(s):  
Banach Space ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Partial Order ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Weak And Strong Convergence ◽  
Convergence Theorems ◽  
New Class ◽  
Krasnoselskii Iteration

<p>In this manuscript we introduce a new class of monotone generalized nonexpansive mappings and establish some weak and strong convergence theorems for Krasnoselskii iteration in the setting of a Banach space with partial order. We consider also an application to the space L<sub>1</sub>([0,1]). Our results generalize and unify the several related results in the literature.</p>

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