In this paper, a new class of general nonlinear variational inclusions involving H-monotone is introduced and studied in Hilbert spaces. By applying the resolvent operator associated with H-monotone, we prove the existence and uniqueness theorems of solution for the general nonlinear variational inclusion, construct an iterative algorithm for computing approximation solution of the general nonl...

In this paper, a new class of (h, η)-proximal mappings for proper functionals in Hilbert spaces is introduced. The existence and Lipschitz continuity of the (h, η)-proximal mappings for proper functionals are proved. A class of generalized nonlinear quasi-variational-like inclusions in Hilbert spaces is introduced. A perturbed three-step iterative algorithm with errors for the generalized nonli...

Multivalued differential equations arise naturally in various branches of modern mathematics, indeed they play a significant role in the description of processes in control theory and non-smooth analysis. Due to their wide applicability in physics, biology, chemistry, and economics, there has recently been an increasing interest in this field. The aim of this Special Session is to outline the r...

We introduce a new iterative method for approximating a locally unique solution of variational inclusions in Banach spaces by using generalized divided differences of the first order. This method extends a method considered by Traub [17] (in the scalar case) and by Potra [12] (in the Banach spaces case) for solving nonlinear equations to variational inclusions. An existence–convergence theorem ...

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...

The resolvent operator approach is applied to address a system of generalized ordered variational inclusions with ⊕ operator in real ordered Banach space. With the help of the resolvent operator technique, Li et al. (J. Inequal. Appl. 2013:514, 2013; Fixed Point Theory Appl. 2014:122, 2014; Fixed Point Theory Appl. 2014:146, 2014; Appl. Math. Lett. 25:1384-1388, 2012; Fixed Point Theory Appl. 2...