 
Summary: TAIWANESE JOURNAL OF MATHEMATICS
Vol. 11, No. 3, pp. 703716, August 2007
This paper is available online at http://www.math.nthu.edu.tw/tjm/
GENERALIZED VARIATIONAL INCLUSIONS AND HRESOLVENT
EQUATIONS WITH HACCRETIVE OPERATORS
Rais Ahmad and Qamrul Hasan Ansari
Abstract. In this paper, we consider a more general form of variational inclu
sions, called generalized variational inclusion (for short, GVI). In connection
with GVI, we also consider a generalized resolvent equation with Hresolvent
operator, called Hresolvent equation (for short, HRE). We suggest itera
tive algorithms to compute the approximate solutions of GVI and HRE. The
existence of a unique solution of GVI and HRE and convergence of itera
tive sequences generated by the proposed algorithms are also studied. Several
special cases are also discussed.
1. INTRODUCTION
In the last decade, variational inclusions, generalized forms of variational in
equalities, have been extensively studied and generalized in various directions to
study a wide class of problems arising in mechanics, optimization, nonlinear pro
gramming, economics, finance and applied sciences, etc; See for example [112]
and references therein. One of the most interesting and important aspects of the
