Viscosity approximation methods for resolvents of accretive operators in Banach spaces

2006 ◽  
Vol 1 (1) ◽  
pp. 135-147 ◽  
Author(s):  
Wataru Takahashi
Keyword(s):  
Banach Spaces ◽  
Approximation Methods ◽  
Accretive Operators ◽  
Viscosity Approximation ◽  
Viscosity Approximation Methods

scholarly journals Viscosity Approximation Methods for a General Variational Inequality System and Fixed Point Problems in Banach Spaces

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 36 ◽  
Author(s):  
Yuanheng Wang ◽  
Chanjuan Pan
Keyword(s):  
Variational Inequality ◽  
Banach Spaces ◽  
Approximation Scheme ◽  
Common Element ◽  
Approximation Methods ◽  
Viscosity Approximation ◽  
Expansive Mapping ◽  
Inequality System ◽  
General Variational Inequality ◽  
Viscosity Approximation Methods

In Banach spaces, we study the problem of solving a more general variational inequality system for an asymptotically non-expansive mapping. We give a new viscosity approximation scheme to find a common element. Some strong convergence theorems of the proposed iterative method are obtained. A numerical experiment is given to show the implementation and efficiency of our main theorem. Our results presented in this paper generalize and complement many recent ones.

scholarly journals Viscosity Approximation Methods for Two Accretive Operators in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Jun-Min Chen ◽  
Tie-Gang Fan
Keyword(s):  
Iterative Scheme ◽  
Convex Banach Space ◽  
Approximation Methods ◽  
Accretive Operators ◽  
Viscosity Approximation ◽  
Uniformly Gâteaux Differentiable Norm ◽  
Strictly Convex Banach Space ◽  
Differentiable Norm ◽  
The Common ◽  
Viscosity Approximation Methods

We introduced a viscosity iterative scheme for approximating the common zero of two accretive operators in a strictly convex Banach space which has a uniformly Gâteaux differentiable norm. Some strong convergence theorems are proved, which improve and extend the results of Ceng et al. (2009) and some others.

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