scholarly journals Approximation of common fixed points of a countable family of continuous pseudocontractions in a uniformly smooth Banach space

2011 ◽  
Vol 24 (12) ◽  
pp. 1998-2004 ◽  
Author(s):  
Gang Cai ◽  
Shangquan Bu
Keyword(s):  
Banach Space ◽  
Fixed Points ◽  
Common Fixed Points ◽  
Countable Family ◽  
Smooth Banach Space ◽  
Uniformly Smooth Banach Space ◽  
Uniformly Smooth

scholarly journals Construction of sunny nonexpansive retractions in Banach spaces

2002 ◽  
Vol 66 (1) ◽  
pp. 9-16 ◽  
Author(s):  
Tomas Dominguez Benavides ◽  
Genaro López Acedo ◽  
Hong-Kun Xu
Keyword(s):  
Banach Space ◽  
Fixed Points ◽  
Banach Spaces ◽  
Convex Subset ◽  
Regularity Condition ◽  
Common Fixed Points ◽  
Sunny Nonexpansive Retraction ◽  
Uniformly Smooth Banach Space ◽  
Uniformly Smooth ◽  
Commutative Family

Let  be a commutative family of nonexpansive self-mappings of a closed convex subset C of a uniformly smooth Banach space X such that the set of common fixed points is nonempty. It is shown that if a certain regularity condition is satisfied, then the sunny nonexpansive retraction from C to F can be constructed in an iterative way.

scholarly journals The Convergence of Mann Iteration for Generalized Φ- hemi-contractive Maps

2020 ◽  
pp. 39-52
Author(s):  
Linxin Li ◽  
Dingping Wu
Keyword(s):  
Banach Space ◽  
Fixed Points ◽  
Iteration Process ◽  
Smooth Banach Space ◽  
Mann Iteration ◽  
Uniformly Smooth Banach Space ◽  
Uniformly Smooth ◽  
Contractive Maps ◽  
Mann Iteration Process

Abstract Charles[1] proved the convergence of Picard-type iterative for generalized Φ− accretive non-self maps in a real uniformly smooth Banach space. Based on the theorems of the zeros of strongly Φ − accretive and fixed points of strongly Φ− hemi-contractive we extend the results to Mann-type iterative and Mann iteration process with errors.

scholarly journals The Convergence of Three-Step Iterative Schemes for Generalized Φ − Hemi-Contractive Mappings and the Comparison of Their Rate of Convergence

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Linxin Li ◽  
Dingping Wu
Keyword(s):  
Banach Space ◽  
Fixed Points ◽  
Rate Of Convergence ◽  
Iterative Process ◽  
Smooth Banach Space ◽  
Iterative Schemes ◽  
Uniformly Smooth Banach Space ◽  
Contractive Mappings ◽  
Uniformly Smooth ◽  
Accretive Mappings

Charles proved the convergence of Picard-type iteration for generalized Φ − accretive nonself-mappings in a real uniformly smooth Banach space. Based on the theorems of the zeros of strongly Φ − quasi-accretive mappings and fixed points of strongly Φ − hemi-contractions, we extend the results to Noor iterative process and SP iterative process for generalized Φ − hemi-contractive mappings. Finally, we analyze the rate of convergence of four iterative schemes, namely, Noor iteration, iteration of Corollary 2, SP iteration, and iteration of Corollary 4.

scholarly journals Local solvability of a constrainedgradient system of total variation

2003 ◽  
Vol 2003 (6) ◽  
pp. 353-365 ◽  
Author(s):  
C. E. Chidume ◽  
H. Zegeye
Keyword(s):  
Banach Space ◽  
Iterative Methods ◽  
Total Variation ◽  
Local Solvability ◽  
Independent Interest ◽  
Smooth Banach Space ◽  
Uniformly Smooth Banach Space ◽  
Uniformly Smooth ◽  
Compact Subsets

SupposeXis a realq-uniformly smooth Banach space andF,K:X→XwithD(K)=F(X)=Xare accretive maps. Under various continuity assumptions onFandKsuch that0=u+KFuhas a solution, iterative methods which converge strongly to such a solution are constructed. No invertibility assumption is imposed onKand the operatorsKandFneed not be defined on compact subsets ofX. Our method of proof is of independent interest.

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