Generalized Monotone Mappings with an Application to Variational Inclusions - Ram, Tirth; Iqbal, Mohd (Communications in Mathematics and Applications, 2022)
In this paper, we study a generalized monotone mapping, which is the sum of cocoercive and monotone mapping. The resolvent operator associated with generalized monotone mapping is defined, and some of its properties are discussed. We employ the equivalent formulation of generalized set-valued variational inclusion problems and resolvent equations to show the existence of a solution. In addition, we create an iterative algorithm for the convergence of resolvent equations and solving generalized set-valued variational inclusion problem. An example has also been provided to support the main result.
Keywords: Monotone mapping; Variational inclusions; Iterative algorithm; Resolvent operator; Semi-inner product space