JIPAM
Generalized Auxiliary Problem Principle and Solvability of a Class of Nonlinear Variational Inequalities Involving Cocoercive and CoLipschitzian Mappings 






Authors: 
Ram U. Verma, 


Keywords:

Generalized auxiliary variational inequality problem, Cocoercive mappings, Approximationsolvability, Approximate solutions, Partially relaxed monotone mappings. 


Date Received:

31/12/00 


Date Accepted:

15/03/01 


Subject Codes: 
49J40



Editors: 
Drumi Bainov, 







Abstract: 
The approximationsolvability of the following class of nonlinear variational inequality (NVI) problems, based on a new generalized auxiliary problem principle, is discussed.
Find an element such that for all where are mappings from a nonempty closed convex subset of a real Hilbert space into , and is a continuous convex functional on The generalized auxiliary problem principle is described as follows: for given iterate and, for constants and ), find such that
where
where is a functional on and the derivative of . ;

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