scholarly journals Parametric general variational-like inequality problem in uniformly smooth Banach space

2006 ◽  
Vol 2006 ◽  
pp. 1-14 ◽  
Author(s):  
K. R. Kazmi ◽  
F. A. Khan
Keyword(s):  
Banach Space ◽  
Smooth Banach Space ◽  
Inequality Problem ◽  
Uniformly Smooth Banach Space ◽  
Uniformly Smooth

scholarly journals A Method for Solving the Variational Inequality Problem and Fixed Point Problems in Banach Spaces

2021 ◽  
Vol 53 ◽  
Author(s):  
Wongvisarut Khuangsatung ◽  
Atid Kangtunyakarn
Keyword(s):  
Banach Space ◽  
Variational Inequality ◽  
Variational Inequality Problem ◽  
Contractive Mapping ◽  
Smooth Banach Space ◽  
Common Element ◽  
Strong Convergence Theorem ◽  
Inequality Problem ◽  
Uniformly Smooth Banach Space ◽  
Uniformly Smooth

The purpose of this research is to modify Halpern iteration’s process for finding a common element of the set of solutions of a variational inequality problem and the set of fixed points of a strictly pseudo contractive mapping in q-uniformly smooth Banach space. We also introduce a new technique to prove a strong convergence theorem for a finite family of strictly pseudo contractive mappings in q-uniformly smooth Banach space. Moreover, we give a numerical result to illustrate the main theorem.

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.

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.

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