Monotone And Accretive Operators With Apply To Variational Inclusions

Based on the importance of variational inequality and variational inclusions in mathematical study and motivated and inspired by the the recent works of [1-28], we discuss the following problems,(1) In Hilbert or Banach spaces, we introduce several classes of variational inclusions and systems of variational inclusions involving monotone or accretive operators which are the generalization and union of many known variational inequality and variational inclusions. In addition, we present a new perturbed iterative algorithm for approximating the solutions of variational inclusions. Our algorithms are new.(2) We establishes necessary and sufficient conditions for operator to be H-accretive operator. Based on these conditions, we introduce and study a new class of generalized set-valued variational inclusions involving H-accretive operators in Banach spaces.(3) We establish the generalized-graph-convergence theory about (h,η)-monotone mappings, and based on the generalized-graph-convergence theory and resolvent operate technique, we suggest a new iterative algorithm to compute approximate solutions of a new generalized nonlinear mixed quasi- variational inclusion involving (h,η)-monotone mappings andα-h-strongly monotone mappings.Key words: variational inequality, variational inclusion; maximalη-monotone mappings; (h,η)-monotone mappings; H-accretive operators; generalized-graph-convergence theory; resolvent operator technique; iterative algorithm; perturb; stable...