• Nonlinear Functional Analysis and Applications
• /
• v.27 no.4
• /
• pp.701-707
• /
• 2022

In this article, we put forward a new type of variational inclusion problem known as resolvent inclusion. An algorithm is given for approximating its solution. The convergence of the algorithm is explained with the help of an example and plots using Matlab.

• Communications of the Korean Mathematical Society
• /
• v.36 no.1
• /
• pp.103-119
• /
• 2021

In this article, we study a system of generalized set-valued parametric ordered variational inclusion problems with operator ⊕ in ordered Banach spaces. We introduce the concept of the resolvent operator associated with (α, λ)-ANODSM set-valued mapping and establish the existence theorem of solution for the system of generalized set-valued parametric ordered variational inclusion problems in ordered Banach spaces. In order to prove the existence of solution, we suggest an iterative algorithm and discuss the convergence analysis under some suitable mild conditions.

• Korean Journal of Mathematics
• /
• v.24 no.2
• /
• pp.199-213
• /
• 2016

The resolvent operator approach of [2] is applied to solve a set-valued variational inclusion problem in ordered Hilbert spaces. The resolvent operator under consideration is called relaxed resolvent operator and we demonstrate some of its properties. To obtain the solution of a set-valued variational inclusion problem, an iterative algorithm is developed and weak-RRD set-valued mapping is used. The problem as well as main result of this paper are more general than many previous problems and results available in the literature.

• Bulletin of the Korean Mathematical Society
• /
• v.41 no.2
• /
• pp.241-256
• /
• 2004

In this paper, we introduce and study a new class of variational inclusions, called the general variational inclusion. We prove the equivalence between the general variational inclusions, the general resolvent equations, and the fixed-point problems, using the resolvent operator technique. This equivalence is used to suggest and analyze a few iterative algorithms for solving the general variational inclusions and the general resolvent equations. Under certain conditions, the convergence analyses are also studied. The results presented in this paper generalize, improve and unify a number of recent results.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.8 no.1
• /
• pp.55-66
• /
• 2004

First the notion of the A-monotonicity is applied to the approximation - solvability of a class of nonlinear variational inclusion problems, and then the convergence analysis is given based on a projection-like method. Results generalize nonlinear variational inclusions involving H-monotone mappings in the Hilbert space setting.

• Honam Mathematical Journal
• /
• v.41 no.1
• /
• pp.207-225
• /
• 2019

In the present paper, we propose some new fractional dynamical systems. These dynamical systems are associated with the variational inclusions involving difference of operators problem. The equivalence between the variational inclusion problems and the fixed point problems and as well as the resolvent equations are used to suggest fractional resolvent dynamical systems and fractional resolvent equation dynamical systems, respectively. We show that these dynamical systems converge ${\alpha}$-exponentially to the unique solution of variational inclusion problems under fewer restrictions imposed on operators and parameters. Several special cases also discussed.

• Nonlinear Functional Analysis and Applications
• /
• v.26 no.4
• /
• pp.749-780
• /
• 2021

In this paper, we give the notion of M(., .)-𝜂-proximal mapping for a nonconvex, proper, lower semicontinuous and subdifferentiable functional on Banach space and prove its existence and Lipschitz continuity. As an application, we introduce and investigate a new system of variational-like inclusions in Banach spaces. By means of M(., .)-𝜂-proximal mapping method, we give the existence of solution for the system of variational inclusions. Further, propose an iterative algorithm for finding the approximate solution of this class of variational inclusions. Furthermore, we discuss the convergence and stability analysis of the iterative algorithm. The results presented in this paper may be further expolited to solve some more important classes of problems in this direction.

• Nonlinear Functional Analysis and Applications
• /
• v.26 no.5
• /
• pp.917-933
• /
• 2021

In this paper, we investigate the behavior and sensitivity analysis of a solution set for a parametric generalized multi-valued nonlinear quasi-variational inclusion problem in a real Hilbert space. For this study, we utilize the technique of resolvent operator and the property of a fixed-point set of a multi-valued contractive mapping. We also examine Lipschitz continuity of the solution set with respect to the parameter under some appropriate conditions.

• Nonlinear Functional Analysis and Applications
• /
• v.28 no.1
• /
• pp.175-203
• /
• 2023

In this paper, we study an iterative algorithm that is based on inertial proximal and contraction methods embellished with relaxation technique, for finding common solution of monotone variational inclusion, and fixed point problems of pseudocontractive mapping in real Hilbert spaces. We establish a strong convergence result of the proposed iterative method based on prediction stepsize conditions, and under some standard assumptions on the algorithm parameters. Finally, some special cases of general problem are given as applications. Our results improve and generalized some well-known and related results in literature.

• Journal of applied mathematics & informatics
• /
• v.28 no.1_2
• /
• pp.451-463
• /
• 2010

In this paper, we introduce and study a class of completely generalized quasi-variational inclusions with fuzzy mappings. A new iterative algorithm for finding the approximate solutions and the convergence criteria of the iterative sequences generated by the algorithm are also given. These results of existence, algorithm and convergence generalize many known results.