Weak and Strong Convergence of an Implicit Iteration Process in Uniformly Convex Banach Spaces

2011 ◽  
Vol 32 (6) ◽  
pp. 682-694
Author(s):  
Isa Yildirim ◽  
Murat Ozdemir
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Iteration Process ◽  
Uniformly Convex ◽  
Weak And Strong Convergence ◽  
Implicit Iteration Process ◽  
Uniformly Convex Banach Spaces ◽  
Implicit Iteration

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 Strong Convergence of Non-Implicit Iteration Process with Errors in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Yan Hao ◽  
Xiaoshuang Wang ◽  
Aihua Tong
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Implicit Iteration Process ◽  
Implicit Iteration

The purpose of this paper is to study the strong convergence of a non-implicit iteration process with errors for asymptoticallyI-nonexpansive mappings in the intermediate sense in the framework of Banach spaces. The results presented in this paper extend and improve the corresponding results recently announced.

scholarly journals A New Faster Iterative Scheme for Numerical Fixed Points Estimation of Suzuki’s Generalized Nonexpansive Mappings

2020 ◽  
Vol 2020 ◽  
pp. 1-9 ◽  
Author(s):  
Shanza Hassan ◽  
Manuel De la Sen ◽  
Praveen Agarwal ◽  
Qasim Ali ◽  
Azhar Hussain
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Iteration Scheme ◽  
Uniformly Convex ◽  
Weak And Strong Convergence ◽  
Uniformly Convex Banach Spaces ◽  
The Stability

The purpose of this paper is to introduce a new four-step iteration scheme for approximation of fixed point of the nonexpansive mappings named as S∗-iteration scheme which is faster than Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, Thakur, and Ullah iteration schemes. We show the stability of our proposed scheme. We present a numerical example to show that our iteration scheme is faster than the aforementioned schemes. Moreover, we present some weak and strong convergence theorems for Suzuki’s generalized nonexpansive mappings in the framework of uniformly convex Banach spaces. Our results extend, improve, and unify many existing results in the literature.

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 Numerical reckoning fixed points for Suzuki’s generalized nonexpansive mappings via new iteration process

Filomat ◽  
2018 ◽  
Vol 32 (1) ◽  
pp. 187-196 ◽  
Author(s):  
Kifayat Ullah ◽  
Muhammad Arshad
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Fixed Points ◽  
Fixed Point Theory ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Point Theory ◽  
Uniformly Convex ◽  
Weak And Strong Convergence ◽  
Uniformly Convex Banach Spaces

In this paper we propose a new three-step iteration process, called M iteration process, for approximation of fixed points. Some weak and strong convergence theorems are proved for Suzuki generalized nonexpansive mappings in the setting of uniformly convex Banach spaces. Numerical example is given to show the efficiency of new iteration process. Our results are the extension, improvement and generalization of many known results in the literature of iterations in fixed point theory.

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