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 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.

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 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 Balls intersection properties of Banach spaces

1992 ◽  
Vol 45 (2) ◽  
pp. 333-342 ◽  
Author(s):  
Dongjian Chen ◽  
Zhibao Hu ◽  
Bor-Luh Lin
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Sufficient Conditions ◽  
Intersection Property ◽  
Necessary And Sufficient Conditions ◽  
Asplund Space ◽  
Necessary And Sufficient

Necessary and sufficient conditions for a Banach space with the Mazur intersection property to be an Asplund space are given. It is proved that Mazur intersection property is determined by the separable subspaces of the space. Corresponding problems for a space to have the ball-generated property are considered. Some comments on possible renorming so that a space having the Mazur intersection property are given.

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 Magnifying Elements in Semigroups of Fixed Point Set Transformations Restricted by an Equivalence Relation

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Thananya Kaewnoi ◽  
Ronnason Chinram ◽  
Montakarn Petapirak
Keyword(s):  
Fixed Point ◽  
Equivalence Relation ◽  
Nonempty Subset ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Fixed Point Set ◽  
Point Set ◽  
Necessary And Sufficient ◽  
Semigroup Of Transformations

Let X be a nonempty set and ρ be an equivalence relation on X . For a nonempty subset S of X , we denote the semigroup of transformations restricted by an equivalence relation ρ fixing S pointwise by E F S X , ρ . In this paper, magnifying elements in E F S X , ρ will be investigated. Moreover, we will give the necessary and sufficient conditions for elements in E F S X , ρ to be right or left magnifying elements.

scholarly journals Necessary and sufficient conditions for common fixed point theorems in fuzzy metric space

2009 ◽  
Vol 42 (4) ◽  
Author(s):  
D. O’Regan ◽  
M. Abbas
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Sufficient Conditions ◽  
Fuzzy Metric Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Common Fixed Point Theorems

AbstractThe aim of this paper is to provide a necessary and sufficient condition for the existence of a common fixed point of three maps

Fixed Point Theorems for Lipspchitzian Semigroups

1989 ◽  
Vol 32 (1) ◽  
pp. 90-97 ◽  
Author(s):  
Hajime ishihara
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Closed Subset ◽  
Fixed Point Theorems ◽  
Nonempty Subset ◽  
Continuous Representation ◽  
Semitopological Semigroup ◽  
Lipschitzian Mappings

AbstractLet U be a nonempty subset of a Banach space, S a left reversible semitopological semigroup, a continuous representation of S as lipschitzian mappings on U into itself, that is for each s ∊ S, there exists ks > 0 such that for x, y ∊ U. We first show that if there exists a closed subset C of U such that then S with lim sups has a common fixed point in a Hilbert space. Next, we prove that the theorem is valid in a Banach space E if lim sups

scholarly journals Common fixed point theorems for a pair of countably condensing mappings in ordered banach spaces

2003 ◽  
Vol 16 (3) ◽  
pp. 243-248 ◽  
Author(s):  
B. C. Dhage ◽  
Donal O'Regan ◽  
Ravi P. Agarwal
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Ordered Banach Space ◽  
Isotone Mappings ◽  
Common Fixed Point Theorems ◽  
Ordered Banach Spaces

In this paper some common fixed point theorems for a pair of multivalued weakly isotone mappings on an ordered Banach space are proved.

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