<p style='text-indent:20px;'>A new strong convergence iterative method for solving a split variational inclusion problem involving bounded linear operator and two maximally monotone mappings is proposed in this article. The study considers an scheme comprised of inertial extrapolation step together with the Mann-type step. A theorem iterates generated by given under suitable conditions. I...

A very general optimization problem with a variational inequality constraint, inequality constraints, and an abstract constraint are studied. Fritz John type and Kuhn–Tucker type necessary optimality conditions involving Mordukhovich coderivatives are derived. Several constraint qualifications for the Kuhn–Tucker type necessary optimality conditions involving Mordukhovich coderivatives are intr...

In order to solve issues that arise in various branches of mathematical analysis, such as split feasibility problems, variational inequality nonlinear optimization issues, equilibrium complementarity selection and matching proving the existence solutions integral differential equations, fixed point theory provides vital tools. this study, we discuss topological structure several fixed-point the...

Variational inequality modeling, analysis and computations are important for many applications, but most of the subject has been developed in a deterministic setting with no uncertainty in a problem’s data. In recent years research has proceeded on a track to incorporate stochasticity in one way or another. However, the main focus has been on a rather limited idea of what a stochastic variation...

This paper introduces an implicit scheme for a   continuous representation of nonexpansive mappings on a closed convex subset of a Hilbert space with respect to a   sequence of invariant means defined on an appropriate space of bounded, continuous real valued functions of the semigroup.   The main result is to    prove the strong convergence of the proposed implicit scheme to the unique solutio...

We introduce a new general system of variational inclusions in Banach spaces and propose a new iterative scheme for finding common element of the set of solutions of the variational inclusion with set-valued maximal monotone mapping and Lipschitzian relaxed cocoercive mapping and the set of fixed point of nonexpansive semigroups in a uniformly convex and 2-uniformly smooth Banach space. Further...

This paper presents a uni­ ed critical-point theory in non-smooth, non-convex and dissipative Hamilton systems. The canonical dual/polar transformation methods and the associated bi-duality and triality theories proposed recently in non-convex variational problems are generalized into fully nonlinear dissipative dynamical systems governed by non-smooth constitutive laws and boundary conditions....