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 Common fixed points of two finite families of nonexpansive mappings by iterations

2015 ◽  
Vol 31 (3) ◽  
pp. 325-331
Author(s):  
HAFIZ FUKHAR-UD-DIN ◽  
◽  
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Uniformly Convex Banach Spaces

We study a Mann type iterative scheme for two finite families of nonexpansive mappings and establish 4− convergence and strong convergence theorems. The obtained results are applicable in uniformly convex Banach spaces (linear domain) and CAT (0) spaces (nonlinear domain) simultaneously.

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 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.

scholarly journals A New Iterative Scheme for Approximation of Fixed Points of Suzuki's Generalized Nonexpansive Mappings

2021 ◽  
Author(s):  
Shivam Rawat ◽  
Ramesh Chandra Dimri ◽  
Ayush Bartwal
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

In this paper, we introduce a new iteration scheme, named as the S**-iteration scheme, for approximation of fixed point of the nonexpansive mappings. This scheme is faster than Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, Thakur, and Ullah iteration schemes. We show the stability of our instigated scheme and give a numerical example to vindicate our claim. We also put forward some weak and strong convergence theorems for Suzuki's generalized nonexpansive mappings in the setting of uniformly convex Banach spaces. Our results comprehend, improve, and consolidate many results in the existing literature.

scholarly journals Convergence theorems of a faster iteration process including multivalued mappings with analytical and numerical examples

Filomat ◽  
2018 ◽  
Vol 32 (16) ◽  
pp. 5665-5677 ◽  
Author(s):  
Birol Gunduz ◽  
Osman Alagoz ◽  
Sezgin Akbulut
Keyword(s):  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Rates Of Convergence ◽  
Multivalued Mappings ◽  
Uniformly Convex ◽  
Weak And Strong Convergence ◽  
Convergence Theorems ◽  
Numerical Examples ◽  
Uniformly Convex Banach Spaces ◽  
Iteration Processes

In this paper, we first give the modified version of the iteration process of Thakur et al. [15] which is faster than Picard, Mann, Ishikawa, Noor, Agarwal et al. [2] and Abbas et al. [1] processes. Secondly, we prove weak and strong convergence theorems of this iteration process for multivalued quasi nonexpansive mappings in uniformly convex Banach spaces. Thirdly, we support our theorems with analytical examples. Finally, we compare rates of convergence for multivalued version of iteration processes mentioned above via a numerical example.

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