K e y w o r d s H a c c r e t i v e operator, Resolvent operator technique, Variational inclusion, Iterative algorithm. 1. I N T R O D U C T I O N A N D P R E L I M I N A R I E S Variational inequalities and variational inclusions are among the most interesting and important mathematical problems and have been studied intensively in the past years since they have wide applications in mechanics,...

A new class of generalized nonlinear variational inclusions involving (A,η)-monotone mappings in the framework of Hilbert spaces is introduced and then based on the generalized resolvent operator technique associated with (A,η)-monotonicity, the approximation solvability of solutions using an iterative algorithm is investigated. Since (A,η)monotonicity generalizes A-monotonicity and H-monotonic...

In this paper, we introduce a generalized system of nonlinear relaxed co-coercive variational inclusions involving (A, η)-monotone mappings in the framework of Hilbert spaces. Based on the generalized resolvent operator technique associated with (A, η)-monotonicity, we consider the approximation solvability of solutions to the generalized system. Since (A, η)-monotonicity generalizes A-monotoni...

ABSTRACT. This paper is devoted to optimal control problem of stochastic switching systems. Dynamics of this processes governed by stochastic differential equations with control terms in the drift and diffusion coefficients. Necessary conditions for optimality of described systems with the restrictions in each interval are obtained. The constraints on the transitions are described by the set of...

In this paper, we introduce a generalized system of nonlinear relaxed cocoercive variational inclusions involving (A, η)-monotone mappings in the framework of Hilbert spaces. Based on the generalized resolvent operator technique associated with (A, η)-monotonicity, we consider the approximation solvability of solutions. Since (A, η)-monotonicity generalizes A-monotonicity and H-monotonicity, ou...

In this paper, a new algorithm for solving a class of variational inclusions involving H-monotone operators is considered in Hilbert spaces. We investigate a general iterative algorithm, which consists of a resolvent operator technique step followed by a suitable projection step. We prove the convergence of the algorithm for a maximal monotone operator without Lipschitz continuity. These result...

The main contributions of this paper is twofold. First, our primary concern to suggest a new iterative algorithm using the P-?-proximal-point mapping technique and Nadler?s for finding approximate solutions system generalized multi-valued nonlinear variational-like inclusions. Under some appropriate conditions imposed on parameters mappings involved in inclusions, strong convergence sequences g...

We introduce a class of η-accretive mappings in a real Banach space and show that the η-proximal point mapping for η-m-accretive mapping is Lipschitz continuous. Further, we develop an iterative algorithm for a class of general variational-like inclusions involving ηaccretive mappings in real Banach space, and discuss its convergence criteria. The class of η-accretivemappings includes several i...

A new system of nonlinear variational inclusions involving A, η -monotone mappings in the framework of Hilbert space is introduced and then based on the generalized resolvent operator technique associated with A, η -monotonicity, the approximation solvability of solutions using an iterative algorithm is investigated. Since A, η -monotonicity generalizes A-monotonicity and Hmonotonicity, our res...

Convergence analysis of a method for variational inclusions M.H. Rashid a b , J.H. Wang c & C. Li a d a Department of Mathematics, Zhejiang University, Hangzhou 310027, P.R. China b Department of Mathematics, Faculty of Science, University of Rajshahi, Rajshahi – 6205, Bangladesh c Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310032, P.R. China d Department of ...