# IJPAM: Volume 22, No. 1 (2005)

**PARTIALLY RELAXED PSEUDOMONOTONE MAPPINGS**

IN APPROXIMATION-SOLVABILITY OF NONLINEAR

VARIATIONAL INEQUALITIES

IN APPROXIMATION-SOLVABILITY OF NONLINEAR

VARIATIONAL INEQUALITIES

Ram U. Verma

Department of Theoretical and Applied Mathematics

The University of Akron

Akron, OH 44325, USA

e-mail: verma99@msn.com

Department of Theoretical and Applied Mathematics

The University of Akron

Akron, OH 44325, USA

e-mail: verma99@msn.com

**Abstract.**Let be a real (finite-dimensional) Hilbert space and be a nonempty closed convex subset of Let be
relaxed pseudomonotone, and let be
relaxed pseudomonotone. Then a class of nonlinear variational inequality (NVI) problems is described as: find an element such that

Let be a solution to the NVI problem and a sequence be generated by a certain iterative algorithm. Suppose that mappings satisfy the following assumptions:

- (i)
- is relaxed pseudomonotone.
- (ii)
- is continuous.
- (iii)
- is relaxed pseudomonotone.
- (iv)
- is continuous.

- (a)
- (b)

**Received: **January 20, 2005

**AMS Subject Classification: **49J40, 65B05

**Key Words and Phrases: **partially relaxed pseudomonotone mappings, approximation-solvability, projection methods, cocoercive mappings, variational inequality problem

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

**ISSN:** 1311-8080

**Year:** 2005

**Volume:** 22

**Issue:** 1