CONVERGENCE ANALYSIS FOR APPROXIMATING SOLUTION OF VARIATIONAL INCLUSION PROBLEM

This article aims to define a new resolvent operator for variational inclusion problems in the framework of  Banach spaces. We design a rapid algorithm using the resolvent operator to approximate the solution of the variational inclusion problem in Banach spaces. Additionally, we show that the algorithm articulated in this article converges faster than the well-known and notable algorithm due to Fang and Huang. To show the superiority and prevalence of the obtained results, we propound a numerical and computational example upholding our claim.  Lastly, a minimization problem is solved with the help of the proposed algorithm, which is the first attempt in the current context of the study

Convergence and stability of iterative algorithm for a new system of (A,η)-accretive mapping inclusions in Banach spaces

AbstractIn this paper, we introduce and study a new system of (A,η)-accretive mapping inclusions in Banach spaces. Using the resolvent operator associated with (A,η)-accretive mappings, we suggest a new general algorithm and establish the existence and uniqueness of solutions for this system of (A,η)-accretive mapping inclusions. Under certain conditions, we discuss the convergence and stability of iterative sequence generated by the algorithm. Our results extend, improve and unify many known results on variational inequalities and variational inclusions

Nonconvex perturbations of maximal monotone differential inclusions

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A New General Iterative Method for Solution of a New General System of Variational Inclusions for Nonexpansive Semigroups in Banach Spaces

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. Furthermore, strong convergence theorems are established under some certain control conditions. As applications, finding a common solution for a system of variational inequality problems and minimization problems is given

Generalized set-valued variational inclusions in q-uniformly smooth Banach spaces

AbstractIn this paper, a class of generalized set-valued variational inclusions in Banach spaces are introduced and studied, which include many variational inclusions studied by others in recent years. By using some new and innovative techniques, several existence theorems for the generalized set-valued variational inclusions in q-uniformly smooth Banach spaces are established, and some perturbed iterative algorithms for solving this kind of set-valued variational inclusions are suggested and analyzed. Our results improve and generalize many known algorithms and results

Random variational-like inclusion and random proximal operator equation for random fuzzy mappings in Banach spaces

In this paper, we introduce and study a random variational-like inclusion and its corresponding random proximal operator equation for random fuzzy mappings. It is established that the random variational-like inclusion problem for random fuzzy mappings is equivalent to a random fixed point problem. We also establish a relationship between random variational-like inclusion and random proximal operator equation for random fuzzy mappings. This equivalence is used to define an iterative algorithm for solving random proximal operator equation for random fuzzy mappings. Through an example, we show that the random Wardrop equilibrium problem is a special case of the random variational-like inclusion problem for random fuzzy mappings