# IJPAM: Volume 1, No. 1 (2002)

**APPROXIMATION SOLVABILITY OF**

NONLINEAR VARIATIONAL INEQUALITIES

BASED ON GENERAL AUXILIARY

PROBLEM PRINCIPLE

NONLINEAR VARIATIONAL INEQUALITIES

BASED ON GENERAL AUXILIARY

PROBLEM PRINCIPLE

Ram U. VermaUniversity of Toledo, Dept. of Mathematics, Toledo, Ohio 43606, USA

International Publications, USA

12046 Coed Drive, Suite A-29

Orlando, Florida 32826, USA

e-mail: verma99@msn.com

International Publications, USA

12046 Coed Drive, Suite A-29

Orlando, Florida 32826, USA

e-mail: verma99@msn.com

**Abstract.**First a general class of auxiliary problem principle is introduced and then it is applied to approximation-solvability of the following class of nonlinear variational inequality problems (NVIP):

Find an element such that

where is a mapping from a nonempty closed convex subset of a reflexive Banach space into its dual , and is a continuous convex functional on . This general class of auxiliary problem principle is described as follows: for a given iterate and for a constant , determine such that

where is -times continuously Frechet-differentiable on .

**Received: **July 22, 2001

**AMS Subject Classification: **49J40

**Key Words and Phrases: **general auxiliary problem principle, auxiliary variational inequality problem, approximation-solvability, approximate solutions

**Source:** International Journal of Pure and Applied Mathematics

**ISSN:** 1311-8080

**Year:** 2002

**Volume:** 1

**Issue:** 1