scholarly journals Viscosity iterative algorithm for variational inequality problems and fixed point problems in a real q-uniformly smooth Banach space

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Gang Cai
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Variational Inequality ◽  
Iterative Algorithm ◽  
Variational Inequality Problems ◽  
Fixed Point Problems ◽  
Smooth Banach Space ◽  
Uniformly Smooth Banach Space ◽  
Uniformly Smooth

CONVERGENCE ANALYSIS ON HYBRID PROJECTION ALGORITHMS FOR EQUILIBRIUM PROBLEMS AND VARIATIONAL INEQUALITY PROBLEMS

2009 ◽  
Vol 14 (3) ◽  
pp. 335-351 ◽  
Author(s):  
Xiaolong Qin ◽  
Yeol Je Cho ◽  
Shin Min Kang
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Variational Inequality ◽  
Iterative Method ◽  
Convergence Analysis ◽  
Equilibrium Problems ◽  
Variational Inequality Problems ◽  
Fixed Point Problems ◽  
Projection Algorithms

In this paper, we consider an iterative method for equilibrium problems, fixed point problems and variational inequality problems in the framework of Banach space. The results presented in this paper improve and extend the corresponding results announced by many others.

scholarly journals Another control condition in an iterative method for nonexpansive mappings

2002 ◽  
Vol 65 (1) ◽  
pp. 109-113 ◽  
Author(s):  
Hong-Kun Xu
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Iterative Method ◽  
Nonexpansive Mapping ◽  
Nonexpansive Mappings ◽  
Smooth Banach Space ◽  
Uniformly Smooth Banach Space ◽  
Uniformly Smooth

We prove the convergence of an iterative method to a fixed point of a nonexpansive mapping in a uniformly smooth Banach space. We are able to relax one of the control conditions of P.L. Lions (1977).

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