H(.,.)-φ-η-Mixed Monotone Mapping with An Application in Semi-Inner Product Space

Abstract

The objective of this work is to proposed a new notion called - - -mixed monotone mappings in semi-inner product spaces and define generalized resolvent operator linked with - - -mixed monotone mappings. Further, we perusal its aspects single-valued property as well as Lipschitz continuity. As an application, we also make an attempt to find the existence of solution of set valued variational inclusion involving nonlinear operators and study the graph convergence of proposed iterative algorithms.