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This paper deals with a new class of nonlinear set valued implicit variational inclusion problems involving (A, η)-monotone mappings in 2-uniformly smooth Banach spaces. Semi-inner product structure has been used to study the (A, η)-monotonicity. Using the generalized resolvent operator technique and the semi-inner product structure, the approximation solvability of the proposed problem is investigated. An iterative algorithm is constructed to approximate the solution of the problem. Convergence analysis of the proposed algorithm is investigated. Similar results are also investigated for variational inclusion problems involving (H, η)-monotone mappings.

Implicit Variational Inclusions and Algorithms Involving (A, η)-monotone Operators in 2-uniformly Smooth Banach Spaces