APPROXIMATION SOLVABILITY OF A PERTURBED MANN ITERATIVE ALGORITHM WITH ERRORS FOR A SYSTEM OF MIXED VARIATIONAL INCLUSIONS INVOLVING $\OPLUS$ OPERATION

BISMA  ZAHOOR; MOHD IQBAL  BHAT; MUDASIR A.  MALIK

APPROXIMATION SOLVABILITY OF A PERTURBED MANN ITERATIVE ALGORITHM WITH ERRORS FOR A SYSTEM OF MIXED VARIATIONAL INCLUSIONS INVOLVING $\OPLUS$ OPERATION

Authors

BISMA ZAHOOR Department of Mathematics, South Campus University of Kashmir, Anantnag-192101, India
MOHD IQBAL BHAT Cluster University Srinagar, Jammu and Kashmir-190008, India
MUDASIR A. MALIK Department of Mathematics, South Campus University of Kashmir, Anantnag-192101, India

Keywords:

Variational Inclusion, $\oplus$-Operation, Resolvent Operator, algorithm, convergence

Abstract

In this paper, we consider a new resolvent operator associated with XOR-NODSM mappings and give some of its facinating properties supported by a well constructed example. As an application, we introduce and study a system of general mixed variational inclusions involving $\oplus$ operation in ordered Hilbert spaces. Further, we propose a perturbed Mann Iterative Algorithm with errors for approximating the solution of this class of problems. Our results can be complemented as the refinenement and generalization of the the corresponding results of recent works.