Convergence Theorems for Suzuki Generalized Nonexpansive Mapping in Banach Spaces

2021 ◽  
Vol 54 ◽  
Author(s):  
Abdulhamit Ekinci ◽  
Seyit Temir
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Convergence Theorems ◽  
Approximate Fixed Point ◽  
Strong Theorems ◽  
Numerical Example ◽  
Generalized Nonexpansive Mapping

In this paper, we study a new iterative scheme to approximate fixed point of Suzuki nonexpansive type mappings in Banach space. We also provesome weak and strong theorems for Suzuki nonexpansive typemappings. Numerical example is given to show the efficiency of newiteration process. The results obtained in this paper improve therecent ones announced by B. S. Thakur et al. \cite{Thakur}, Ullahand Arschad \cite{UA}.

scholarly journals Fixed Point and Weak Convergence Theorems for(α,β)-Hybrid Mappings in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Tian-Yuan Kuo ◽  
Jyh-Chung Jeng ◽  
Young-Ye Huang ◽  
Chung-Chien Hong
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Weak Convergence ◽  
Banach Spaces ◽  
Bregman Distance ◽  
Convergence Theorems ◽  
Convergence Problem

We introduce the class of(α,β)-hybrid mappings relative to a Bregman distanceDfin a Banach space, and then we study the fixed point and weak convergence problem for such mappings.

scholarly journals Convergence theorems of a scheme for I-asymptotically quasi-nonexpansive type mapping in Banach space

2015 ◽  
Vol 97 (111) ◽  
pp. 239-251
Author(s):  
Seyit Temir
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Recent Work ◽  
Nonempty Subset ◽  
Sufficient Conditions ◽  
Convergence Theorems ◽  
Type Mapping ◽  
Necessary And Sufficient

Let X be a Banach space. Let K be a nonempty subset of X. Let T : K ? K be an I-asymptotically quasi-nonexpansive type mapping and I : K ? K be an asymptotically quasi-nonexpansive type mappings in the Banach space. Our aim is to establish the necessary and sufficient conditions for the convergence of the Ishikawa iterative sequences with errors of an I-asymptotically quasi-nonexpansive type mappping in Banach spaces to a common fixed point of T and I. Also, we study the convergence of the Ishikawa iterative sequences to common fixed point for nonself I-asymptotically quasinonexpansive type mapping in Banach spaces. The results presented in this paper extend and generalize some recent work of Chang and Zhou [1], Wang [19], Yao and Wang [20] and many others.

scholarly journals Fixed point iteration for asymptotically quasi-nonexpansive mappings in Banach spaces

2005 ◽  
Vol 2005 (11) ◽  
pp. 1685-1692 ◽  
Author(s):  
Somyot Plubtieng ◽  
Rabian Wangkeeree
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Convex Subset ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Nonempty Closed Convex Subset ◽  
Convex Banach Space ◽  
Uniformly Convex ◽  
Completely Continuous

Suppose thatCis a nonempty closed convex subset of a real uniformly convex Banach spaceX. LetT:C→Cbe an asymptotically quasi-nonexpansive mapping. In this paper, we introduce the three-step iterative scheme for such map with error members. Moreover, we prove that ifTis uniformlyL-Lipschitzian and completely continuous, then the iterative scheme converges strongly to some fixed point ofT.

scholarly journals Fixed-Point Theorems for Mean Nonexpansive Mappings in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Zhanfei Zuo
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonexpansive Mappings ◽  
Uniqueness Theorems ◽  
Existence And Uniqueness Theorems ◽  
Approximate Fixed Point

We define a mean nonexpansive mappingTonXin the sense thatTx-Ty≤ax-y+bx-Ty,a,b≥0,a+b≤1. It is proved that mean nonexpansive mapping has approximate fixed-point sequence, and, under some suitable conditions, we get some existence and uniqueness theorems of fixed point.

scholarly journals Strong Convergence Theorems for Equilibrium Problems and Fixed Point Problems in Hilbert Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-13
Author(s):  
Jian-Wen Peng ◽  
Yan Wang
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Common Element ◽  
Convergence Theorems

We introduce an Ishikawa iterative scheme by the viscosity approximate method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in Hilbert space. Then, we prove some strong convergence theorems which extend and generalize S. Takahashi and W. Takahashi's results (2007).

scholarly journals Results on a faster iterative scheme for a generalized monotone asymptotically

2021 ◽  
Vol 20 ◽  
pp. 356-370
Author(s):  
Athraa Najeb Abed ◽  
Salwa Salman Abed II
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Iterative Scheme ◽  
Ordered Banach Space

This article devoted to present results on convergence of  Fibonacci-Halpern scheme (shortly, FH) for monotone asymptotically αn-nonexpansive  mapping (shortly, ma αn-n mapping) in partial ordered Banach space (shortly, POB space). Which are auxiliary theorem for demi-close's proof of this type of mappings, weakly convergence of increasing FFH-scheme to a fixed point with aid monotony of a norm and  Σn+=∞1 λn= +∞, λn =min{hn , (1-hn)} where hn ⸦ (0,1)   where is associated with FH-scheme for an integer n>0 more than that, convergence amounts to be strong by using Kadec-Klee property and finally, prove that this scheme is weak-w2 stable up on suitable status.

Convergence Theorems for Accretive Operators in Banach Spaces

2011 ◽  
Vol 50-51 ◽  
pp. 224-228
Author(s):  
Yan Guo ◽  
Ji Wei He ◽  
Yan Mei Yang
Keyword(s):  
Banach Space ◽  
Variational Inequality ◽  
Nonexpansive Mapping ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Accretive Operator ◽  
Common Element ◽  
Accretive Operators ◽  
Uniformly Smooth ◽  
Strongly Accretive Operator

In this paper, a new iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping and the set of the variational inequality for an inverse-strongly accretive operator in a 2-uniformly smooth Banach space was introduced . It was verified that the sequence converged to a common element of two sets.

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 Strong Convergence Theorems for Two Total Quasi-ϕ-Asymptotically Nonexpansive Mappings in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Xi-bing He ◽  
Xiao-jian Hui ◽  
Hui Xing
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Mathematical Programming ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Hybrid Method ◽  
Nonexpansive Mappings ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive

The purpose of this paper is to establish some strong convergence theorems for a common fixed point of two total quasi-ϕ-asymptotically nonexpansive mappings in Banach space by means of the hybrid method in mathematical programming. The results presented in this paper extend and improve on the corresponding ones announced by Martinez-Yanes and Xu (2006), Plubtieng and Ungchittrakool (2007), Qin et al. (2009), and many others.

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