Some Iterative Methods for Fixed Point Problems

2013 ◽  
pp. 273-300 ◽  
Author(s):  
Q. H. Ansari ◽  
D. R. Sahu
Keyword(s):  
Fixed Point ◽  
Iterative Methods ◽  
Fixed Point Problems

scholarly journals Strong Convergence Analysis of Iterative Algorithms for Solving Variational Inclusions and Fixed-Point Problems of Pseudocontractive Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Zhangsong Yao ◽  
Yan-Kuen Wu ◽  
Ching-Feng Wen
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Convergence Analysis ◽  
Iterative Methods ◽  
Iterative Algorithms ◽  
Fixed Point Problems ◽  
Variational Inclusions ◽  
Type Method ◽  
Common Solution ◽  
Mild Conditions

Iterative methods for solving variational inclusions and fixed-point problems have been considered and investigated by many scholars. In this paper, we use the Halpern-type method for finding a common solution of variational inclusions and fixed-point problems of pseudocontractive operators. We show that the proposed algorithm has strong convergence under some mild conditions.

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.

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