General system for strongly accretive nonlinear variational inequalities in q-uniformly smooth Banach spaces

2007 ◽  
Vol 2 ◽  
pp. 1121-1127
Author(s):  
Rudong Chen ◽  
Linfang Xing
Keyword(s):  
Variational Inequalities ◽  
Banach Spaces ◽  
General System ◽  
Uniformly Smooth ◽  
Uniformly Smooth Banach Spaces

scholarly journals Algorithms for General System of Generalized Resolvent Equations with Corresponding System of Variational Inclusions

2012 ◽  
Vol 2012 ◽  
pp. 1-24
Author(s):  
Lu-Chuan Ceng ◽  
Ching-Feng Wen
Keyword(s):  
Banach Spaces ◽  
General System ◽  
Approximate Solutions ◽  
Variational Inclusions ◽  
Convergence Criteria ◽  
Generalized Resolvent ◽  
Resolvent Equations ◽  
Uniformly Smooth ◽  
Uniformly Smooth Banach Spaces ◽  
Generalized Resolvent Equations

Very recently, Ahmad and Yao (2009) introduced and considered a system of generalized resolvent equations with corresponding system of variational inclusions in uniformly smooth Banach spaces. In this paper we introduce and study a general system of generalized resolvent equations with corresponding general system of variational inclusions in uniformly smooth Banach spaces. We establish an equivalence relation between general system of generalized resolvent equations and general system of variational inclusions. The iterative algorithms for finding the approximate solutions of general system of generalized resolvent equations are proposed. The convergence criteria of approximate solutions of general system of generalized resolvent equations obtained by the proposed iterative algorithm are also presented. Our results represent the generalization, improvement, supplement, and development of Ahmad and Yao corresponding ones.

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