ITERATIVE ALGORITHM FOR A SYSTEM OF MULTI-VALUED VARIATIONAL INCLUSIONS INVOLVING $(B, \phi)$-MONOTONE MAPPINGS IN BANACH SPACES

K. R.  KAZMI; NAEEM  AHMAD

ITERATIVE ALGORITHM FOR A SYSTEM OF MULTI-VALUED VARIATIONAL INCLUSIONS INVOLVING $(B, \phi)$-MONOTONE MAPPINGS IN BANACH SPACES

Authors

K. R. KAZMI Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India
NAEEM AHMAD Department of Mathematics, P.O. Box 2014, Skaka, Al-Jouf University, Kingdom of Saudi Arabia

Keywords:

System of multi-valued variational inclusions, (B,φ)-monotone mappings, Iterative algorithm and convergence analysis

Abstract

In this paper, we introduce a new class of resolvent mappings for $(B, \phi)$-monotone mappings in Banach space, which is a natural and important generalization of a class of resolvent mappings studied in [X.-P. Luo, N.-J. Huang; A new class of variational inclusions with B-monotone operators in Banach spaces, J. Comput. Appl. Math. 233 (2010), 1888-1896]. We study some properties of this new class of resolvent mappings and by making use of it, we discuss the existence and iterative approximation of solutions of a system of multi-valued variational inclusions. The method and results presented in this paper improve and generalize many known results in the literature.