A-Monotonicity And Its Role In Nonlinear Variational Inclusions And System Of Set-Valued Variational Inclusions

This paper gives a new class of completely generalized set-valued strongly nonlinear mixed implicit quasi-variational inclusions and a new system of generalized set-valued variational inclusions involving A-monotone mappings in Hilbert spaces. By studying the properties of A-monotone mapping and its resolvent operator, we propose some new algorithms for solving these variational inclusions and system of variational inclusions. The convergence analysis of the iterative sequences generated by these algorithms is also discussed. The results of this paper are general in nature and improve and extend a broad range of consequences in the literature.This paper is divided into the following three chapters:In chapter one, we mainly introduce some basic concepts and the origin, development and application of A-monotone mapping. By studying the properties of A-monotone mapping, we define the resolvent operator for A-monotone mapping and discuss its Lipschitz continuity.In chapter two, a new class of completely generalized set-valued strongly nonlinear mixed implicit quasi-variational inclusions involving A-monotone mapping is introduced and investigated in Hilbert spaces. By applying resolvent operator technique for A-monotone mapping, we construct a new iterative algorithm for approximating the solutions of the class of completely generalized set-valued strongly nonlinear mixed implicit quasi-variational inclusions. The convergence analysis of the iterative sequences generated by the algorithm is also discussed.In chapter three, a new system of generalized set-valued variational inclusions involving A-monotone mappings is given in Hilbert spaces. A new iterative algorithm for solving this system of generalized ser-valued variational inclusions is proposed and its strong convergence criteria is also established under suitable assumptions.