In this paper, we consider completely generalized nonlinear quasi-variational-like inclusions in Banach spaces and propose an Ishikawa type iterative algorithm for computing their approximate solutions by applying the new notion of Jη-proximal mapping given in [R. Ahmad, A.H. Siddiqi, Z. Khan, Proximal point algorithm for generalized multi-valued nonlinear quasi-variational-like inclusions in B...

The purpose of this work, we present a new iterative algorithm for finding a common of the set of solutions of a mixed equilibrium problem, the set of a variational inclusion and the set of fixed point of nonexpansive mapping in a real Hilbert space. Under suitable conditions, some strong convergence theorems for approximating a common element of the above three sets are obtained. The results p...

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...

In this paper, by using a resolvent operator technique of (H,η)monotone mappings, we study the behavior and sensitivity of the solutions of the system of parametric variational inclusions with (H,η)monotone operators in Hilbert spaces. Our results extend and improve the main results obtained by Agarwal, Huang and Tan [R. P. Agarwal, N. J. Huang and M. Y. Tan, Sensitivity analysis for a new syst...

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.

In this paper, the concepts of well-posednesses and Hadamard well-posedness for a family of mixed variational inequalities are studied. Also, some metric characterizations of them are presented and some relations between well-posedness and Hadamard well-posedness of a family of mixed variational inequalities is studied. Finally, a relation between well-posedness for the family of mixed variatio...

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...