Iterative Algorithms for a Generalized System of Mixed Variational-Like Inclusion Problems and Altering Points Problem

In this article, we introduce and study a generalized system of mixed variational-like inclusion problems involving αβ-symmetric η-monotone mappings. We use the resolvent operator technique to calculate the approximate common solution of the generalized system of variational-like inclusion problems involving αβ-symmetric η-monotone mappings and a fixed point problem for nonlinear Lipchitz mappings. We study strong convergence analysis of the sequences generated by proposed Mann type iterative algorithms. Moreover, we consider an altering points problem associated with a generalized system of variational-like inclusion problems. To calculate the approximate solution of our system, we proposed a parallel S-iterative algorithm and study the convergence analysis of the sequences generated by proposed parallel S-iterative algorithms by using the technique of altering points problem. The results presented in this paper may be viewed as generalizations and refinements of the results existing in the literature.

An Iterative Algorithm for the Nonlinear MC2 Model with Variational Inequality Method

The multiple criteria and multiple constraint level (MC 2 ) model is a useful tool to deal with the decision programming problems, which concern multiple decision makers and uncertain resource constraint levels. In this paper, by regarding the nonlinear MC 2 problems as a class of mixed implicit variational inequalities, we develop an iterative algorithm to solve the nonlinear MC 2 problems through the resolvent operator technique. The convergence of the generated iterative sequence is analyzed and discussed by a calculation example, and the stability of Algorithm 1 is also verified by error propagation. By comparing with two other MC 2 -algorithms, Algorithm 1 performs well in terms of number of iterations and computation complexity.

Approximation solvability for a system of implicit nonlinear variational inclusions with Η-monotone operators

In this paper, we introduce and study a new system of variational inclusions which is called a system of nonlinear implicit variational inclusion problems with A-monotone and H-monotone operators in semi-inner product spaces. We define the resolvent operator associated with A-monotone and H-monotone operators and prove its Lipschitz continuity. Using resolvent operator technique, we prove the existence and uniqueness of solution for this new system of variational inclusions. Moreover, we suggest an iterative algorithm for approximating the solution of this system and discuss the convergence analysis of the sequences generated by the iterative algorithm under some suitable conditions.

Stable Perturbed Iterative Algorithms for Solving New General Systems of Nonlinear Generalized Variational Inclusion in Banach Spaces

We introduce and study a new general system of nonlinear variational inclusions involving generalizedm-accretive mappings in Banach space. By using the resolvent operator technique associated with generalizedm-accretive mappings due to Huang and Fang, we prove the existence theorem of the solution for this variational inclusion system in uniformly smooth Banach space, and discuss convergence and stability of a class of new perturbed iterative algorithms for solving the inclusion system in Banach spaces. Our results presented in this paper may be viewed as an refinement and improvement of the previously known results.

Iterative Algorithms for New General Systems of Set-Valued Variational Inclusions Involving(A,η)-Maximal Relaxed Monotone Operators

We introduce and study a class of new general systems of set-valued variational inclusions involving(A,η)-maximal relaxed monotone operators in Hilbert spaces. By using the general resolvent operator technique associated with(A,η)-maximal relaxed monotone operators, we construct some new iterative algorithms for finding approximation solutions to the general system of set-valued variational inclusion problem and prove the convergence of this algorithm. Our results improve and extend some known results.

A Wiener-Hopf Dynamical System for Mixed Equilibrium Problems

We suggest and analyze dynamical systems associated with mixed equilibrium problems by using the resolvent operator technique. We show that these systems have globally asymptotic property. The concepts and results presented in this paper extend and unify a number of previously known corresponding concepts and results in the literature.

Three-Step Iterative Method for Completely Generalized Set-Valued Strongly Nonlinear Quasi-Variational Inclusions

In this paper, we introduce and study a new class of completely generalized set-valued strongly nonlinear variational inclusions in Hilbert spaces and establish the equivalence between this variational inclusion and the fixed-point problem by using the resolvent operator technique for maximal monotone mapping. We construct a new three-step iterative algorithm and show the existence of solution for this variational inclusion and the convergence of the iterative method generated by the iterative method.

Strong Convergence of Iterative Algorithm for a New System of GeneralizedH·,·-η-Cocoercive Operator Inclusions in Banach Spaces

We introduce and study a new system of generalizedH·,·-η-cocoercive operator inclusions in Banach spaces. Using the resolvent operator technique associated withH·,·-η-cocoercive operators, we suggest and analyze a new generalized algorithm of nonlinear set-valued variational inclusions and establish strong convergence of iterative sequences produced by the method. We highlight the applicability of our results by examples in function spaces.

Generalized -Cocoercive Operators and Generalized Set-Valued Variational-Like Inclusions

We investigate a new class of cocoercive operators named generalized -cocoercive operators in Hilbert spaces. We prove that generalized -cocoercive operator is single-valued and Lipschitz continuous and extends the concept of resolvent operators associated with -cocoercive operators to the generalized -cocoercive operators. Some examples are given to justify the definition of generalized -cocoercive operators. Further, we consider a generalized set-valued variational-like inclusion problem involving generalized -cocoercive operator. In terms of the new resolvent operator technique, we give the approximate solution and suggest an iterative algorithm for the generalized set-valued variational-like inclusions. Furthermore, we discuss the convergence criteria of iterative algorithm under some suitable conditions. Our results can be viewed as a generalization of some known results in the literature.

Generalized System for Relaxed Cocoercive Mixed Variational Inequalities and Iterative Algorithms in Hilbert Spaces

The approximate solvability of a generalized system for relaxed co- coercive mixed variational inequality is studied by using the resolvent operator technique. The results presented in this paper extend and improve the main results of Chang et al.[1], He and Gu [2] and Verma [3, 4].