scholarly journals STRONG CONVERGENCE OF AN ITERATIVE ALGORITHM FOR SYSTEMS OF VARIATIONAL INEQUALITIES AND FIXED POINT PROBLEMS IN q-UNIFORMLY SMOOTH BANACH SPACES

2012 ◽  
Vol 20 (2) ◽  
pp. 225-237
Author(s):  
Jae Ug Jeong
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Iterative Algorithm ◽  
Fixed Point Problems ◽  
Uniformly Smooth ◽  
Systems Of Variational Inequalities ◽  
Uniformly Smooth Banach Spaces

MODIFIED HALPERN ITERATIVE ALGORITHM FOR NONEXPANSIVE MAPPINGS II

2011 ◽  
Vol 04 (04) ◽  
pp. 683-694
Author(s):  
Mengistu Goa Sangago
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Algorithm ◽  
Nonexpansive Mappings ◽  
Convergence Conditions ◽  
Uniformly Smooth ◽  
Additional Control ◽  
Uniformly Smooth Banach Spaces

Halpern iterative algorithm is one of the most cited in the literature of approximation of fixed points of nonexpansive mappings. Different authors modified this iterative algorithm in Banach spaces to approximate fixed points of nonexpansive mappings. One of which is Yao et al. [16] modification of Halpern iterative algorithm for nonexpansive mappings in uniformly smooth Banach spaces. Unfortunately, some deficiencies are found in the Yao et al. [16] control conditions imposed on the modified iteration to obtain strong convergence. In this paper, counterexamples are constructed to prove that the strong convergence conditions of Yao et al. [16] are not sufficient and it is also proved that with some additional control conditions on the parameters strong convergence of the iteration is obtained.

scholarly journals Iterative Solutions for Solving Variational Inequalities and Fixed-Point Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Li-Jun Zhu ◽  
Naseer Shahzad ◽  
Asim Asiri
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Fixed Point Problems ◽  
Suggested Algorithm ◽  
Iterative Solutions

In this paper, we are interested in variational inequalities and fixed-point problems in Hilbert spaces. We present an iterative algorithm for finding a solution of the studied variational inequalities and fixed-point problems. We show the strong convergence of the suggested algorithm.

scholarly journals Hierarchical Fixed Point Problems in Uniformly Smooth Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Lu-Chuan Ceng ◽  
Ching-Feng Wen ◽  
Chin-Tzong Pang
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Problems ◽  
Approximation Methods ◽  
Viscosity Approximation ◽  
Uniformly Smooth ◽  
Hierarchical Fixed Point ◽  
Viscosity Approximation Methods ◽  
Uniformly Smooth Banach Spaces ◽  
Hierarchical Fixed Point Problems

We propose some relaxed implicit and explicit viscosity approximation methods for hierarchical fixed point problems for a countable family of nonexpansive mappings in uniformly smooth Banach spaces. These relaxed viscosity approximation methods are based on the well-known viscosity approximation method and hybrid steepest-descent method. We obtain some strong convergence theorems under mild conditions.

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