In this article, we introduce and consider some new classes of general quasi variational inclusions, which provide us with unified, natural, novel simple framework to a wide class unrelated problems arising in pure applied sciences. We prove that the inclusions are equivalent fixed point problems. This alternative formulation is used discuss existence solution as well propose iterative methods....

The purpose of this paper is to introduce a general iterative method for finding solutions of a general system of variational inclusions with Lipschitzian relaxed cocoercive mappings. Strong convergence theorems are established in strictly convex and 2-uniformly smooth Banach spaces. Moreover, we apply our result to the problem of finding a common fixed point of a countable family of strict pse...

In this paper we study evolution inclusions generated by time dependent convex subdifferentials, with the orientor field F depending on a parameter. Under reasonable hypotheses on the data, we show that the solution set S(λ) is both Vietoris and Hausdorff metric continuous in λ ∈ Λ. Using these results, we study the variational stability of a class of nonlinear parabolic optimal control problems.

In this paper, we study the behavior and sensitivity analysis of the solution set for a new system of parametric generalized nonlinear mixed quasi-variational inclusions with (A, η)-accretive mappings in quniformly smooth Banach spaces. The present results improve and extend many known results in the literature.

Based on the notion of A−maximal relaxed accretiveness, the convergence analysis of the over-relaxed proximal point algorithm in the context of the approximating the solutions of a class of nonlinear variational inclusions is explored. Moreover, some results on the general firm nonexpansiveness are also investigated. The obtained results are general and application-oriented in nature.

In this paper, by using a resolvent operator technique of (H,η)-monotone mappings, we study the behavior and sensitivity of the solutions for a system of variational inclusions with (H,η)-monotone operators in Hilbert spaces. Mathematics Subject Classification: 49J40, 47H19, 47H10

This paper studies optimal control problems for dynamical systems governed by neutral functional-differential inclusions that linearly depend on delayed velocity variables. Developing the method of discrete approximations, we derive new necessary optimality conditions for such problems in both EulerLagrange and Hamiltonian forms. The results obtained are expressed in terms of advanced generaliz...