- GENERAL VARIATIONAL INCLUSIONS AND GENERAL RESOLVENT EQUATIONS
- Liu, Zeqing ; Ume, Jeong-Sheok ; Kang, Shin-Min ;
- Bulletin of the Korean Mathematical Society, volume 41, issue 2, 2004, Pages 241~256
- DOI : 10.4134/BKMS.2004.41.2.241

Abstract

In this paper, we introduce and study a new class of variational inclusions, called the general variational inclusion. We prove the equivalence between the general variational inclusions, the general resolvent equations, and the fixed-point problems, using the resolvent operator technique. This equivalence is used to suggest and analyze a few iterative algorithms for solving the general variational inclusions and the general resolvent equations. Under certain conditions, the convergence analyses are also studied. The results presented in this paper generalize, improve and unify a number of recent results.