scholarly journals An extragradient approximation method for variational inequality problem on fixed point problem of nonexpensive mappings and monotone mappings

2012 ◽  
pp. 45-59
Author(s):  
Alongkot Suvarnamani ◽  
Mongkol Tatong
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Approximation Method ◽  
Variational Inequality Problem ◽  
Fixed Point Problem ◽  
Monotone Mappings ◽  
Point Problem ◽  
Inequality Problem

scholarly journals Existence and convergence theorem for fixed point problem of various nonlinear mappings and variational inequality problems without some assumptions

Filomat ◽  
2018 ◽  
Vol 32 (1) ◽  
pp. 305-309 ◽  
Author(s):  
Wongvisarut Khuangsatung ◽  
Atid Kangtunyakarn
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Convergence Theorem ◽  
Variational Inequality Problem ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Common Element ◽  
Strong Convergence Theorem ◽  
Point Problem ◽  
Inequality Problem

The purpose of this article, we give a necessary and sufficient condition for the modified Mann iterative process in order to obtain a strong convergence theorem for finding a common element of the set of fixed point of a finite family of nonexpansive mappings and variational inequality problem in Hilbert space without the conditions ?Ni=1 Fix(Ti)? VI(C,A)??. Moreover, we utilize our main result to fixed point problems of strictly pseudocontractive mappings and the set of solutions of variational inequality problem.

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