Iterative Methods for Equilibrium and Fixed Point Problems for Nonexpansive Semigroups in Hilbert Spaces

2009 ◽  
Vol 146 (2) ◽  
pp. 491-509 ◽  
Author(s):  
F. Cianciaruso ◽  
G. Marino ◽  
L. Muglia
Keyword(s):  
Fixed Point ◽  
Iterative Methods ◽  
Hilbert Spaces ◽  
Fixed Point Problems ◽  
Nonexpansive Semigroups

scholarly journals Strong Convergence of the Iterative Methods for Hierarchical Fixed Point Problems of an Infinite Family of Strictly Nonself Pseudocontractions

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Wei Xu ◽  
Yuanheng Wang
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Strong Convergence ◽  
Iterative Methods ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Infinite Family ◽  
Fixed Point Problems ◽  
Hierarchical Fixed Point ◽  
Hierarchical Fixed Point Problems

This paper deals with a new iterative algorithm for solving hierarchical fixed point problems of an infinite family of pseudocontractions in Hilbert spaces byyn=βnSxn+(1-βn)xn,xn+1=PC[αnf(xn)+(1-αn)∑i=1∞μi(n)Tiyn], and∀n≥0, whereTi:C↦His a nonselfki-strictly pseudocontraction. Under certain approximate conditions, the sequence{xn}converges strongly tox*∈⋂i=1∞F(Ti), which solves some variational inequality. The results here improve and extend some recent results.

Sign in / Sign up

Export Citation Format

Share Document