Andrzej Cegielski, "Iterative methods for fixed point problems in Hilbert spaces"

2015 ◽  
Vol 51 (1) ◽  
Author(s):  
Kazimierz Goebel
Keyword(s):  
Fixed Point ◽  
Iterative Methods ◽  
Hilbert Spaces ◽  
Fixed Point Problems

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.

scholarly journals Convergence of Two Splitting Projection Algorithms in Hilbert Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 922
Author(s):  
Marwan A. Kutbi ◽  
Abdul Latif ◽  
Xiaolong Qin
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Fixed Point Problems ◽  
Monotone Mappings ◽  
Projection Algorithms ◽  
Convergence Theorems ◽  
Expansive Mapping ◽  
Computational Errors ◽  
Zero Points

The aim of this present paper is to study zero points of the sum of two maximally monotone mappings and fixed points of a non-expansive mapping. Two splitting projection algorithms are introduced and investigated for treating the zero and fixed point problems. Possible computational errors are taken into account. Two convergence theorems are obtained and applications are also considered in Hilbert spaces

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