The Journal of the Indian Mathematical Society

N. K. Sahu ¹, C. Nahak ¹, S. Nanda ²

Affiliations
1 Department of Mathematics, Indian Institute of Technology, Kharagpur - 721302, IN
2 KIIT University, Bhubaneswar -751 024, IN

Abstract

This paper deals with a general class of nonlinear implicit variational inclusion problems in 2-uniformly smooth Banach spaces. Applying the generalized resolvent operator technique involving A-maximal m-relaxed monotonicity, the existence and uniqueness solution of the proposed problem is established. Using the generalized graph convergence, an implicit algorithm is developed that approximates the unique solution. Finally, the convergence analysis of the proposed algorithm is accomplished. Similar results are also explored for other classes of maximal monotone mappings.

Keywords

Variational Inclusion, Maximal Monotone Mapping, Resolvent Operator, Semi-Inner Product Space.

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