It is well known that the implicit resolvent equations are equivalent to the quasivariational inclusions. We use this alternative equivalent formulation to study the sensitivity of the quasi-variational inclusions without assuming the differentiability of the given data. Since the quasivariational inclusions include classical variational inequalities, quasi (mixed) variational inequalities, and...

In this paper, we introduce and study a new system of variational inclusions with B-monotone operators in Banach spaces. By using the proximal mapping associated with Bmonotone operator, we construct a new iterative algorithm for approximating the solution of this system of variational inclusions. We also prove the existence of solutions and the convergence of the sequences generated by the alg...

We introduce and consider some new systems of extended general variational inclusions involving six different operators. We establish the equivalence between this system of extended general variational inclusions and the fixed points using the resolvent operators technique. This equivalent formulation is used to suggest and analyze some new iterativemethods for this system of extended general v...

In this paper, we consider a more general form of generalized nonlinear variational inclusions and prove the existence of solutions for these generalized nonlinear variational inclusions with and without convexity.

Based on the very recent work by Censor-Gibali-Reich [7], we propose an extension of their new variational problem (Split Variational Inequality Problem) to monotone variational inclusions. Relying on the Krasnoselskii-Mann Theorem for averaged operators, we analyze an algorithm for solving a new split monotone inclusions under weaker conditions. Our results improve and develop previously discu...

By using the notion of Jη-proximal mapping for a nonconvex, lower semicontinuous, ηsubdifferentiable proper functional in reflexive Banach spaces, we introduce and study a class of generalized set-valued variational-like inclusions in Banach spaces and show their equivalences with a class of Wiener-Hopf equations. We propose two new iterative algorithms for the class of generalized set-valued v...

A new system of nonlinear fuzzy variational inclusions involving A, η -accretive mappings in uniformly smooth Banach spaces is introduced and studiedmany fuzzy variational and variational inequality inclusion problems as special cases of this system. By using the resolvent operator technique associated with A, η -accretive operator due to Lan et al. and Nadler’s fixed points theorem for set-val...

The main purpose of this paper is to introduce and study a new class of generalized nonlinear setvalued quasi-variational inclusions system involving A, η -accretive mappings in Banach spaces. By using the resolvent operator due to Lan-Cho-Verma associated with A, η -accretive mappings and the matrix analysis method, we prove the convergence of a new hybrid proximal point three-step iterative a...

In this paper, we introduce and study a new system of nonlinear A-monotone multivalued variational inclusions in Hilbert spaces. By using the concept and properties of A-monotone mappings, and the resolvent operator technique associated with A-monotone mappings due to Verma, we construct a new iterative algorithm for solving this system of nonlinear multivalued variational inclusions associated...

A new class of generalized nonlinear set-valued quasivariational inclusions involving generalizedm-accretive mappings in Banach spaces are studied, which included many variational inclusions studied by others in recent years. By using the properties of the resolvent operator associated with generalized m-accretive mappings, we established the equivalence between the generalized nonlinear set-va...