scholarly journals Approximation of Solutions of an Equilibrium Problem in a Banach Space

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Hecai Yuan ◽  
Guohong Shi
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Equilibrium Problem ◽  
Iterative Algorithm ◽  
Smooth Banach Space ◽  
Convergence Theorems ◽  
Strictly Convex ◽  
Uniformly Smooth Banach Space ◽  
Uniformly Smooth

An equilibrium problem is investigated based on a hybrid projection iterative algorithm. Strong convergence theorems for solutions of the equilibrium problem are established in a strictly convex and uniformly smooth Banach space which also enjoys the Kadec-Klee property.

Iterative Methods for Strictly Pseudo-Contractive Mappings

2013 ◽  
Vol 333-335 ◽  
pp. 1402-1405
Author(s):  
Yang Liu ◽  
Yan Hao
Keyword(s):  
Banach Space ◽  
Iterative Method ◽  
Strong Convergence ◽  
Iterative Methods ◽  
Smooth Banach Space ◽  
Convergence Theorems ◽  
Uniformly Smooth Banach Space ◽  
Contractive Mappings ◽  
Uniformly Smooth

The aim of this work is to consider an iterative method for a-strict pseudo-contractions. Strong convergence theorems are established in a real 2-uniformly smooth Banach space.

scholarly journals On the Convergence of Mann and Ishikawa Iterative Processes for Asymptoticallyϕ-Strongly Pseudocontractive Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Xuewu Wang ◽  
Giuseppe Marino ◽  
Luigi Muglia
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Iterative Process ◽  
Smooth Banach Space ◽  
Iterative Processes ◽  
Uniformly Smooth Banach Space ◽  
Pseudocontractive Mappings ◽  
Uniformly Smooth ◽  
Ishikawa Iterative Process

We prove the equivalence and the strong convergence of (1) the modified Mann iterative process and (2) the modified Ishikawa iterative process for asymptoticallyϕ-strongly pseudocontractive mappings in a uniformly smooth Banach space.

scholarly journals A Note on Implicit and Explicit Mann Iterative Processes for Asymptotically -Strongly Pseudocontractive Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Luigi Muglia ◽  
Yonghong Yao
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Iterative Process ◽  
Smooth Banach Space ◽  
Iterative Processes ◽  
Uniformly Smooth Banach Space ◽  
Pseudocontractive Mappings ◽  
Uniformly Smooth ◽  
Implicit And Explicit

In this paper we prove the equivalence and the strong convergence of an explicit Mann iterative process and a modified implicit iterative process for asymptotically -strongly pseudocontractive mappings in a uniformly smooth Banach space.

scholarly journals Approximation of viscosity zero points of accretive operators in a Banach space

Filomat ◽  
2014 ◽  
Vol 28 (10) ◽  
pp. 2175-2184
Author(s):  
Sun Cho ◽  
Shin Kang
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Iterative Algorithm ◽  
Accretive Operators ◽  
Convergence Theorems ◽  
Computational Errors ◽  
Zero Points

In this paper, zero points of m-accretive operators are investigated based on a viscosity iterative algorithm with double computational errors. Strong convergence theorems for zero points of m-accretive operators are established in a Banach space.

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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