Three-Step Iterative Algorithms for Multivalued Quasi Variational Inclusions (original) (raw)
Computers & Mathematics with Applications, 2010
Extended generalized nonlinear mixed quasi-variational inclusions Perturbed N-step iterative algorithm with mixed errors Resolvent operator technique Variational convergence q-uniformly smooth Banach spaces a b s t r a c t This paper introduces a new system of extended generalized nonlinear mixed quasivariational inclusions involving A-maximal m-relaxed η-accretive (so called (A, η)-accretive (Lan et al. (2006) [37])) mappings in q-uniformly smooth Banach spaces. By using the resolvent operator technique for A-maximal m-relaxed η-accretive mappings due to Lan et al., we establish the existence and uniqueness of solution for this system of extended generalized nonlinear mixed quasi-variational inclusions and construct a new perturbed N-step iterative algorithm with mixed errors for solving the mentioned system. We also prove the convergence of the sequences generated by our algorithms in q-uniformly smooth Banach spaces. The results presented in this paper extend and improve some known results in the literature.
Convergence of Iterative Schemes for Multivalued Quasi-Variational Inclusions
Positivity, 2004
Relying on the resolvent operator method and using Nadler's theorem, we suggest and analyze a class of iterative schemes for solving multivalued quasi-variational inclusions. In fact, by considering problems involving composition of mutivalued operators and by replacing the usual compactness condition by a weaker one, our result can be considered as an improvement and a signi cant extension of previously known results in this eld. 2000 AMS Subject Classi cation: 49J40, 90C33.
An iterative algorithm for generalized nonlinear variational inclusions
Applied Mathematics Letters, 2000
In this paper, we consider the generalized nonlinear variational inclusions for nonclosed and nonbounded valued operators and define an iterative algorithm for finding the approximate solutions of this class of variational inclusions. We also establish that the approximate solutions obtained by our algorithm converge to the exact solution of the generalized nonlinear variational inclusion.
Iterative algorithm for a system of nonlinear variational-like inclusions
Computers & Mathematics with Applications, 2004
In this paper, we consider a system of nonlinear variational-like inclusions (SNVLI) in Hilbert spaces. In particular, SNVLI reduces to a variational inclusion, an extension of variational inclusion studied by Hassouni and Moudafi . Using fixed-point method, we suggest an iterative algorithm for finding an approximate solution to SNVLI. Further, we prove the existence of solution and discuss convergence criteria for the approximate solution of SNVLI. The theorems presented in this paper improve and unify many known results of variational inclusions and variational inequalities, see for example [1-3]. (~) 2004 Elsevier Ltd. All rights reserved.
Algorithms for Solving System of Extended General Variational Inclusions and Fixed Points Problems
Abstract and Applied Analysis, 2012
We introduce a new system of extended general nonlinear variational inclusions with different nonlinear operators and establish the equivalence between the aforesaid system and the fixed point problem. By using this equivalent formulation, we prove the existence and uniqueness theorem for solution of the system of extended general nonlinear variational inclusions. We suggest and analyze a new resolvent iterative algorithm to approximate the unique solution of the system of extended general nonlinear variational inclusions which is a fixed point of a nearly uniformly Lipschitzian mapping. Subsequently, the convergence analysis of the proposed iterative algorithm under some suitable conditions is considered. Furthermore, some related works to our main problem are pointed out and discussed.
Symmetry, 2021
The goal of this study was to show how a modified variational inclusion problem can be solved based on Tseng’s method. In this study, we propose a modified Tseng’s method and increase the reliability of the proposed method. This method is to modify the relaxed inertial Tseng’s method by using certain conditions and the parallel technique. We also prove a weak convergence theorem under appropriate assumptions and some symmetry properties and then provide numerical experiments to demonstrate the convergence behavior of the proposed method. Moreover, the proposed method is used for image restoration technology, which takes a corrupt/noisy image and estimates the clean, original image. Finally, we show the signal-to-noise ratio (SNR) to guarantee image quality.
Journal of Inequalities and Applications, 2014
The purpose of this paper is to introduce new approximation methods for solutions of generalized non-accretive multi-valued mixed quasi-variational inclusion systems involving ( A , η ) -accretive mappings in q-uniformly smooth Banach spaces and, by using the new resolvent operator technique associated with ( A , η ) -accretive mappings, Nadler’s fixed point theorem and Liu’s inequality, we prove some existence theorems of solutions for our systems by constructing the new Mann iterative algorithm. Further, we study the stability of the iterative sequence generated by the perturbed iterative algorithms. The results presented in this paper improve and generalize the corresponding results of recent works given by some authors.
Symmetry, 2021
This manuscript aims to study a generalized, set-valued, mixed-ordered, variational inclusion problem involving H(·,·)-compression XOR-αM-non-ordinary difference mapping and relaxed cocoercive mapping in real-ordered Hilbert spaces. The resolvent operator associated with H(·,·)-compression XOR-αM-non-ordinary difference mapping is defined, and some of its characteristics are discussed. We prove existence and uniqueness results for the considered generalized, set-valued, mixed-ordered, variational inclusion problem. Further, we put forward a three-step iterative algorithm using a ⊕ operator, and analyze the convergence of the suggested iterative algorithm under some mild assumptions. Finally, we reconfirm the existence and convergence results by an illustrative numerical example.
Solving Variational Inclusions by a Method Obtained Using a Multipoint Iteration Formula
Revista Matemática Complutense, 2009
This paper deals with variational inclusions of the form: 0 ∈ f (x) + F (x) where f is a single function admitting a second order Fréchet derivative and F is a set-valued map acting in Banach spaces. We prove the existence of a sequence (x k) satisfying 0 ∈ f (x k)+ M i=1 ai∇f x k +βi(x k+1 −x k) (x k+1 −x k)+F (x k+1) where the single-valued function involved in this relation is an approximation of the function f based on a multipoint iteration formula and we show that this method is locally cubically convergent.
Generalized multivalued nonlinear quasi-variational like inclusions
In this paper, we suggest and analyze a class of iterative schemes for solving generalized multivalued nonlinear quasi-variational like inclusion problems using the concept of η-subdifferential and η-proximal mappings of a proper functional on Hilbert spaces. A detailed convergence analysis of our method is also included.