Approximation Solvability for a System of Nonlinear Variational Type Inclusions in Banach Spaces.

In this paper, we consider a system of nonlinear variational type inclusions involving (H, η, φ)-monotone operators in real Banach spaces. Further, we define a proximal operator associated with an (H; η; φ)-monotone operator and show that it is single valued and Lipschitz continuous. Using proximal point operator techniques, we prove the existence and uniqueness of a solution and suggest an iterative algorithm for the system of nonlinear variational type inclusions. Furthermore, we discuss the convergence of the iterative sequences generated by the algorithms. [ABSTRACT FROM AUTHOR]