scholarly journals Weak and Strong Convergence Theorems for Nonexpansive Mappings in Banach Spaces

2008 ◽  
Vol 2008 ◽  
pp. 1-8 ◽  
Author(s):  
Jing Zhao ◽  
Songnian He ◽  
Yongfu Su
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Weak And Strong Convergence ◽  
Convergence Theorems

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 Weak and strong convergence theorems for three Suzuki’s generalized nonexpansive mappings

2021 ◽  
Vol 110 (124) ◽  
pp. 121-129
Author(s):  
Seyit Temir
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Weak And Strong Convergence ◽  
Convergence Theorems

We introduce a new iterative scheme for finding a common fixed point of three Suzuki?s generalized nonexpansive mappings in Banach spaces. We establish weak and strong convergence theorems for three Suzuki?s generalized nonexpansive mappings. The results obtained extend and improve the recent ones announced by Ali et al., Maniu and Thakur et al..

scholarly journals Approximating Fixed Points of Bregman Generalized α-Nonexpansive Mappings

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 709 ◽  
Author(s):  
Kanikar Muangchoo ◽  
Poom Kumam ◽  
Yeol Je Cho ◽  
Sompomg Dhompongsa ◽  
Sakulbuth Ekvittayaniphon
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Weak And Strong Convergence ◽  
Convergence Theorems ◽  
Iterative Schemes ◽  
Numerical Example ◽  
New Class

In this paper, we introduce a new class of Bregman generalized α -nonexpansive mappings in terms of the Bregman distance. We establish several weak and strong convergence theorems of the Ishikawa and Noor iterative schemes for Bregman generalized α -nonexpansive mappings in Banach spaces. A numerical example is given to illustrate the main results of fixed point approximation using Halpern’s algorithm.

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>

scholarly journals Weak and Strong Convergence Theorems for Zeroes of Accretive Operators in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Yanlai Song ◽  
Luchuan Ceng
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Recent Literature ◽  
Nonexpansive Mappings ◽  
Common Element ◽  
Inclusion Problem ◽  
Accretive Operators ◽  
Weak And Strong Convergence ◽  
Convergence Theorems ◽  
Variational Inclusion Problem

The purpose of this paper is to present two new forward-backward splitting schemes with relaxations and errors for finding a common element of the set of solutions to the variational inclusion problem with two accretive operators and the set of fixed points of nonexpansive mappings in infinite-dimensional Banach spaces. Under mild conditions, some weak and strong convergence theorems for approximating this common elements are proved. The methods in the paper are novel and different from those in the early and recent literature. Our results can be viewed as the improvement, supplementation, development, and extension of the corresponding results in the very recent literature.

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