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TAIWANESE JOURNAL OF MATHEMATICS Vol. 11, No. 3, pp. 703-716, August 2007
 

Summary: TAIWANESE JOURNAL OF MATHEMATICS
Vol. 11, No. 3, pp. 703-716, August 2007
This paper is available online at http://www.math.nthu.edu.tw/tjm/
GENERALIZED VARIATIONAL INCLUSIONS AND H-RESOLVENT
EQUATIONS WITH H-ACCRETIVE 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 H-resolvent
operator, called H-resolvent equation (for short, H-RE). We suggest itera-
tive algorithms to compute the approximate solutions of GVI and H-RE. The
existence of a unique solution of GVI and H-RE 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 [1-12]
and references therein. One of the most interesting and important aspects of the

  

Source: Ansari, Qamrul Hasan - Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals

 

Collections: Mathematics