Viscosity Approximation Method for Nonexpansive Semigroups in Banach Spaces

2013 ◽  
Vol 42 (1) ◽  
pp. 63-72 ◽  
Author(s):  
Duong Viet Thong ◽  
Le Anh Dung
Keyword(s):  
Banach Spaces ◽  
Approximation Method ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Nonexpansive Semigroups

scholarly journals Viscosity approximation method for solving variational inequality problem in real Banach spaces

2021 ◽  
pp. 1-20
Author(s):  
Godwin Ugwunnadi
Keyword(s):  
Variational Inequality ◽  
Banach Spaces ◽  
Approximation Method ◽  
Variational Inequality Problem ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Inequality Problem ◽  
Mild Conditions ◽  
Uniformly Smooth ◽  
Uniformly Smooth Banach Spaces

In this paper, we study the implicit and inertial-type viscosity approximation method for approximating a solution to the hierarchical variational inequality problem. Under some mild conditions on the parameters, we prove that the sequence generated by the proposed methods converges strongly to a solution of the above-mentioned problem in $q$-uniformly smooth Banach spaces. The results obtained in this paper generalize and improve many recent results in this direction.

scholarly journals The Meir-Keeler Type for Solving Variational Inequalities and Fixed Points of Nonexpansive Semigroups in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Phayap Katchang ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Strong Convergence Theorem ◽  
Accretive Mapping ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Nonexpansive Semigroups ◽  
Strongly Accretive Mapping

The aim of this paper is to introduce a new iterative scheme for finding common solutions of the variational inequalities for an inverse strongly accretive mapping and the solutions of fixed point problems for nonexpansive semigroups by using the modified viscosity approximation method associate with Meir-Keeler type mappings and obtain some strong convergence theorem in a Banach spaces under some parameters controlling conditions. Our results extend and improve the recent results of Li and Gu (2010), Wangkeeree and Preechasilp (2012), Yao and Maruster (2011), and many others.

scholarly journals A Viscosity Approximation Method with a Weakly Contractive Mapping of General Iterative Processes for Nonexpansive Semigroups in Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-17
Author(s):  
Pongsakorn Sunthrayuth ◽  
Chanan Sudsukh ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Approximation Method ◽  
Contractive Mapping ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Iterative Processes ◽  
Weakly Contractive Mapping ◽  
Weakly Contractive

We introduce a new viscosity approximation method with a weakly contractive mapping of general iterative processes for finding common fixed point of nonexpansive semigroups {T(t):t∈ℝ+} in the framework of Banach spaces. We proved that under some mild conditions these iterative processes converge strongly to the common fixed point of {T(t):t∈ℝ+}, which is the unique solution of some variational inequality. The results obtained in this paper extend and improve on the recent results of Li et al. (2009), Chen and He (2007), and many others as special cases.

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