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

PARTIALLY RELAXED PSEUDOMONOTONE MAPPINGS
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

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.
Then the sequence converges to for , and the following estimates hold:
(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