This paper deals with a new system of nonlinear variational inclusion problems involving (A, η)-maximal relaxed monotone and relative (A, η)-maximal monotone mappings in 2-uniformly smooth Banach spaces. Using the generalized resolvent operator technique, the approximation solvability of the proposed problem is investigated. An iterative algorithm is constructed to approximate the solution of t...

Based on the notion of (A,η)-accretive mappings and the resolvent operators associated with (A,η)-accretive mappings due to Lan et al., we study a new class of multivalued nonlinear variational inclusion problemswith (A,η)-accretivemappings in Banach spaces and construct some new iterative algorithms to approximate the solutions of the nonlinear variational inclusion problems involving (A,η)-ac...

In this paper, we introduce a new class of monotone operators − (H(·, ·), η)monotone operators, which generalize many existing monotone operators. The resolvent operator associated with an (H(·, ·), η)monotone operator is defined and its Lipschitz continuity is presented. As an application, we also consider a new generalized mixed variational inclusion involving (H(·, ·), η)-monotone operators ...

In this paper, we prove the existence of solutions for a class of nonlinear variational inclusion problems in semi-inner product spaces. We construct an iterative algorithm for approximating the solution for the class of variational inclusions involving A-monotone operators by using the resolvent operator technique.

In this paper, we consider generalized mixed co-quasi-variational inclusions and propose an iterative algorithm for computing their approximate solutions by using definition of J-proximal mapping given in [9]. We prove that the approximate solutions obtained by proposed algorithm converge to the exact solution of our co-quasi-variational inclusion. Some special cases are also discussed. AMS Sub...

This paper deals with a new class of nonlinear set valued implicit variational inclusion problems involving (A, η)-monotone mappings in 2-uniformly smooth Banach spaces. Semi-inner product structure has been used to study the (A, η)-monotonicity. Using the generalized resolvent operator technique and the semi-inner product structure, the approximation solvability of the proposed problem is inve...

Variational data assimilation is performed using either a T40 18 layer version of the National Meteorological Center spectral model or a limited-area shallow-water equations model, with operationally analyzed fields as well as simulated datasets. Issues of incomplete observations, control of gravitational oscillations, and inclusion of “on-off” physical processes are addressed in the framework ...

We consider a multiparameter discrete inclusion and we prove that the reachable set of a certain variational multiparameter discrete inclusion is a derived cone in the sense of Hestenes to the reachable set of the discrete inclusion. This result allows to obtain sufficient conditions for local controllability along a reference trajectory and a new proof of the minimum principle for an optimizat...

In this paper, using Lipschitz continuity of general (H, η)-monotone operators, a type of implicit variational-like inclusion problems in uniformly smooth Banach spaces are solved.