Three-Step Iterative Algorithms for Multivalued Quasi Variational Inclusions

AbstractIn this paper, we suggest and analyze some new classes of three-step iterative algorithms for solving multivalued quasi variational inclusions by using the resolvent equations technique. New iterative algorithms include the Ishikawa, Mann, and Noor iterations for solving variational inclusions (inequalities) and optimization problems as special cases. The results obtained in this paper represent an improvement and a significant refinement of previously known results

An iterative method for generalized set-valued nonlinear mixed quasi-variational inequalities

AbstractThis paper presents an iterative method for solving the generalized nonlinear set-valued mixed quasi-variational inequality, a problem class that was introduced by Huang et al. (Comp. Math. Appl. 40 (2–3) (2000) 205–215). The method incorporates step size controls that enable application to problems where certain set-valued mappings do not always map to nonempty closed bounded sets

Convergence and stability of iterative algorithm for a new system of (A,η)-accretive mapping inclusions in Banach spaces

AbstractIn this paper, we introduce and study a new system of (A,η)-accretive mapping inclusions in Banach spaces. Using the resolvent operator associated with (A,η)-accretive mappings, we suggest a new general algorithm and establish the existence and uniqueness of solutions for this system of (A,η)-accretive mapping inclusions. Under certain conditions, we discuss the convergence and stability of iterative sequence generated by the algorithm. Our results extend, improve and unify many known results on variational inequalities and variational inclusions

Existence and Stability of Iterative Algorithm for a System of Random Set-Valued Variational Inclusion Problems Involving ( A

We introduce and study a class of a system of random set-valued variational inclusion problems. Some conditions for the existence of solutions of such problems are provided, when the operators are contained in the classes of generalized monotone operators, so-called (A,m,η)-monotone operator. Further, the stability of the iterative algorithm for finding a solution of the considered problem is also discussed