scholarly journals Modified three step iterative process with errors for common fixed point of generalized asymptotically quasi-nonexpansive mappings

2012 ◽  
Vol 43 (4) ◽  
pp. 577-586
Author(s):  
Seyit Temir ◽  
Hükmi Kızıltunc
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Convergence Results ◽  
The Common

In this paper we introduce to modified three step iterative process with errors for approximating the common fixed point for generalized asymptotically quasi-nonexpansive mappings and prove some strong convergence results for the iterative sequences iterations with errors in real Banach spaces. The results obtained in this paper extend and improve the recent ones announced by Lan \cite{Lan}, Nantadilok \cite{Nan}, Saluja and Nashine \cite{SN} and Yang et all. \cite{LY} and many others.

scholarly journals Strong Convergence Theorems for a Common Fixed Point of a Family of Asymptoticallyk-Strict Pseudocontractive Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
H. Zegeye ◽  
N. Shahzad
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Iterative Process ◽  
Finite Family ◽  
Important Class ◽  
Convergence Theorems ◽  
Nonlinear Operators ◽  
Pseudocontractive Mappings

We provide an iterative process which converges strongly to a common fixed point of finite family of asymptoticallyk-strict pseudocontractive mappings in Banach spaces. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.

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 Strong Convergence Theorems for Quasi-Bregman Nonexpansive Mappings in Reflexive Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Mohammed Ali Alghamdi ◽  
Naseer Shahzad ◽  
Habtu Zegeye
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Maximal Monotone ◽  
Finite Family ◽  
Monotone Mappings ◽  
Reflexive Banach Spaces ◽  
Convergence Theorems

We study a strong convergence for a common fixed point of a finite family of quasi-Bregman nonexpansive mappings in the framework of real reflexive Banach spaces. As a consequence, convergence for a common fixed point of a finite family of Bergman relatively nonexpansive mappings is discussed. Furthermore, we apply our method to prove strong convergence theorems of iterative algorithms for finding a common solution of a finite family equilibrium problem and a common zero of a finite family of maximal monotone mappings. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

scholarly journals Strong Convergence Theorems for Split Common Fixed Point Problem of Bregman Generalized Asymptotically Nonexpansive Mappings in Banach Spaces

2019 ◽  
pp. 35-50
Author(s):  
Yusuf Ibrahim
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Common Fixed Point Problem ◽  
Asymptotically Nonexpansive ◽  
Split Common Fixed Point

In this paper, a new iterative scheme is introduced and also strong convergence theorems for solving split common fixed point problem for uniformly continuous Bregman generalized asymptotically nonexpansive mappings in uniformly convex and uniformly smooth Banach spaces are presented. The results are proved without the assumption of semicompactness property and or Opial condition

scholarly journals Convergence theorems for Bregman strongly nonexpansive mappings in reflexive Banach spaces

Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1525-1536 ◽  
Author(s):  
Habtu Zegeye
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Convergence Theorem ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Strong Convergence Theorem ◽  
Monotone Mappings ◽  
Convergence Theorems

In this paper, we study a strong convergence theorem for a common fixed point of a finite family of Bregman strongly nonexpansive mappings in the framework of reflexive real Banach spaces. As a consequence, we prove convergence theorem for a common fixed point of a finite family of Bergman relatively nonexpansive mappings. Furthermore, we apply our method to prove strong convergence theorems of iterative algorithms for finding a common zero of a finite family of Bregman inverse strongly monotone mappings and a solution of a finite family of variational inequality problems.

scholarly journals Implicit Ishikawa Approximation Methods for Nonexpansive Semigroups in CAT(0) Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Zhi-bin Liu ◽  
Yi-shen Chen ◽  
Xue-song Li ◽  
Yi-bin Xiao
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Nonexpansive Mappings ◽  
Nonexpansive Semigroup ◽  
Approximation Methods ◽  
Ishikawa Iteration ◽  
Nonexpansive Semigroups ◽  
Convergence Results ◽  
Iteration Processes

This paper is devoted to the convergence of the implicit Ishikawa iteration processes for approximating a common fixed point of nonexpansive semigroup in CAT(0) spaces. We obtain theΔ-convergence results of the implicit Ishikawa iteration sequences for a family of nonexpansive mappings in CAT(0) spaces. Under certain and different conditions, we also get the strong convergence theorems of implicit Ishikawa iteration sequences for nonexpansive semigroups in the CAT(0) spaces. The results presented in this paper extend and generalize some previous results.

scholarly journals Fixed Point Approximation of Nonexpansive Mappings on a Nonlinear Domain

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Safeer Hussain Khan
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Hyperbolic Space ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Convergence Results ◽  
Uniformly Convex Banach Spaces ◽  
Uniformly Convex Hyperbolic Space

We use a three-step iterative process to prove some strong andΔ-convergence results for nonexpansive mappings in a uniformly convex hyperbolic space, a nonlinear domain. Three-step iterative processes have numerous applications and hyperbolic spaces contain Banach spaces (linear domains) as well as CAT(0) spaces. Thus our results can be viewed as extension and generalization of several known results in uniformly convex Banach spaces as well as CAT(0) spaces.

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..

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