scholarly journals Approximation Analysis for a Common Fixed Point of Finite Family of Mappings Which Are Asymptoticallyk-Strict Pseudocontractive in the Intermediate Sense

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
H. Zegeye ◽  
N. Shahzad
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Iterative Process ◽  
Convex Sets ◽  
Common Fixed Points ◽  
Finite Family ◽  
Important Class ◽  
Pseudocontractive Mappings ◽  
Approximation Analysis ◽  
Uniformly Continuous

We introduce an iterative process which converges strongly to a common fixed point of a finite family of uniformly continuous asymptoticallyki-strict pseudocontractive mappings in the intermediate sense fori=1,2,…,N. The projection ofx0onto the intersection of closed convex setsCnandQnfor eachn≥1is not required. Moreover, the restriction that the interior of common fixed points is nonempty is not required. 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 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 a Common Fixed Point of a Finite Family of Bregman Weak Relativity Nonexpansive Mappings in Reflexive Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Habtu Zegeye ◽  
Naseer Shahzad
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Important Class ◽  
Reflexive Banach Spaces ◽  
Nonlinear Operators ◽  
Relatively Nonexpansive Mappings ◽  
Relatively Nonexpansive

We introduce an iterative process for finding an element of a common fixed point of a finite family of Bregman weak relatively nonexpansive mappings. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.

scholarly journals An Iterative Approximation Method for a Common Fixed Point of Two Pseudocontractive Mappings

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Habtu Zegeye
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Approximation Method ◽  
Finite Family ◽  
Convex Minimization Problem ◽  
Iterative Approximation ◽  
Pseudocontractive Mappings ◽  
The Common ◽  
Iterative Approximation Method ◽  
Fixed Point Sets

We introduce an iterative process for finding an element in the common fixed point sets of two continuous pseudocontractive mappings. As a consequence, we provide an approximation method for a common fixed point of a finite family of pseudocontractive mappings. Furthermore, our convergence theorem is applied to a convex minimization problem. Our theorems extend and unify most of the results that have been proved for this class of nonlinear mappings.

scholarly journals Convergence of implicit iterative process for a finite family of I-nonexpansive mappings

2009 ◽  
Vol 42 (1) ◽  
Author(s):  
Seyit Temir ◽  
Goknur Aykanat
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Finite Family

AbstractWe prove that an implicit iterative process converges weakly and strongly to a common fixed point of a finite family of

scholarly journals Approximating common fixed points of finite family of asymptotically nonexpansive non-self mappings

Filomat ◽  
2008 ◽  
Vol 22 (2) ◽  
pp. 23-42
Author(s):  
G.S. Saluja
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Common Fixed Points ◽  
Convex Banach Space ◽  
Finite Family ◽  
Uniformly Convex ◽  
Asymptotically Nonexpansive ◽  
Nonexpansive Retract ◽  
Bounded Sequences ◽  
Condition B

Let K be a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T1 , T2 , ... , TN : K ? E be N asymptotically nonexpansive nonself mappings with sequences {rin} such that ??(n=1) rin < ?, for all 1 ? i ? N and n n=1 n F = ?N(i-1) F (Ti) ? ?. Let {?in}, {?in} and {?in} are sequences in [0, 1] with i=1 ?in + ?in + ?in = 1 for all i = 1, 2, ... , N . From arbitrary x1 ? K , define the sequence {xn} iteratively by (6), where {uin} are bounded sequences in K with ??(n=1) uin < ?. (i) If the dual E*of E has the Kadec-Klee property, then {xn} converges weakly to a common fixed point x*? F ; (ii) if {T1 , T2 , ... , TN} satisfies condition (B), then {xn} converges strongly to a common fixed point x*? F. .

scholarly journals Convergence Results for a Common Solution of a Finite Family of Equilibrium Problems and Quasi-Bregman Nonexpansive Mappings in Banach Space

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
G. C. Ugwunnadi ◽  
Bashir Ali
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Equilibrium Problem ◽  
Iterative Process ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Common Solution ◽  
Convergence Results

We introduce an iterative process for finding common fixed point of finite family of quasi-Bregman nonexpansive mappings which is a unique solution of some equilibrium problem.

scholarly journals Strong Convergence Theorems for a Common Fixed Point of a Finite Family of Pseudocontractive Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
O. A. Daman ◽  
H. Zegeye
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Iteration Method ◽  
Finite Family ◽  
Convergence Theorems ◽  
Ishikawa Iteration ◽  
Pseudocontractive Mappings ◽  
Nonlinear Mappings

It is our purpose, in this paper, to prove strong convergence of Halpern-Ishikawa iteration method to a common fixed point of finite family of Lipschitz pseudocontractive mappings. There is no compactness assumption imposed either onCor onT. The results obtained in this paper improve most of the results that have been proved for this class of nonlinear mappings.

Implicit iterative process for common fixed point of a finite family of asymptotically nonexpansive mappings

2008 ◽  
Vol 45 (2) ◽  
pp. 235-250
Author(s):  
Feng Gu
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Finite Family ◽  
Weak And Strong Convergence ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Implicit Iteration

The purpose of this paper is to study the weak and strong convergence of implicit iteration process to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of [1,2,4–9,11–15].

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