scholarly journals System of Nonlinear Set-Valued Variational Inclusions Involving a Finite Family ofH(·,·)-Accretive Operators in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Prapairat Junlouchai ◽  
Somyot Plubtieng
Keyword(s):  
Banach Spaces ◽  
Resolvent Operator ◽  
Iterative Scheme ◽  
Finite Family ◽  
Strong Convergence Theorem ◽  
Operator Technique ◽  
Variational Inclusions ◽  
Accretive Operators ◽  
Resolvent Operator Technique ◽  
The Resolvent Operator

We study a new system of nonlinear set-valued variational inclusions involving a finite family ofH(·,·)-accretive operators in Banach spaces. By using the resolvent operator technique associated with a finite family ofH(·,·)-accretive operators, we prove the existence of the solution for the system of nonlinear set-valued variational inclusions. Moreover, we introduce a new iterative scheme and prove a strong convergence theorem for finding solutions for this system.

scholarly journals An iterative algorithm for generalized nonlinear variational inclusions with relaxed strongly accretive mappings in Banach spaces

2004 ◽  
Vol 2004 (20) ◽  
pp. 1035-1045 ◽  
Author(s):  
A. H. Siddiqi ◽  
Rais Ahmad
Keyword(s):  
Banach Spaces ◽  
Iterative Algorithm ◽  
Resolvent Operator ◽  
Existence Of Solutions ◽  
Operator Technique ◽  
Variational Inclusions ◽  
Special Cases ◽  
Accretive Mappings ◽  
Resolvent Operator Technique ◽  
The Resolvent Operator

We use Nadler's theorem and the resolvent operator technique form-accretive mappings to suggest an iterative algorithm for solving generalized nonlinear variational inclusions with relaxed strongly accretive mappings in Banach spaces. We prove the existence of solutions for our inclusions without compactness assumption and the convergence of the iterative sequences generated by the algorithm in real Banach spaces. Some special cases are also discussed.

scholarly journals --Accretive Mappings and a New System of Generalized Variational Inclusions with --Accretive Mappings in Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
Sayyedeh Zahra Nazemi
Keyword(s):  
Banach Spaces ◽  
Resolvent Operator ◽  
Lipschitz Continuity ◽  
Operator Technique ◽  
Variational Inclusions ◽  
New Class ◽  
Accretive Mappings ◽  
Resolvent Operator Technique ◽  
The Resolvent Operator ◽  
New System

We introduce a new class of generalized accretive mappings, named --accretive mappings, in Banach spaces. We define a resolvent operator associated with --accretive mappings and show its Lipschitz continuity. We also introduce and study a new system of generalized variational inclusions with --accretive mappings in Banach spaces. By using the resolvent operator technique associated with --accretive mappings, we construct a new iterative algorithm for solving this system of generalized variational inclusions in Banach spaces. We also prove the existence of solutions for the generalized variational inclusions and the convergence of iterative sequences generated by algorithm. Our results improve and generalize many known corresponding results.

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

2018 ◽  
Vol 51 (1) ◽  
pp. 241-254
Author(s):  
Jong Kyu Kim ◽  
Muhammad Iqbal Bhat
Keyword(s):  
Iterative Algorithm ◽  
Resolvent Operator ◽  
Monotone Operators ◽  
Inner Product ◽  
Operator Technique ◽  
Variational Inclusions ◽  
Inclusion Problems ◽  
Resolvent Operator Technique ◽  
The Resolvent Operator ◽  
New System

AbstractIn 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.

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

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Saud M. Alsulami ◽  
Eskandar Naraghirad ◽  
Nawab Hussain
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Resolvent Operator ◽  
Operator Technique ◽  
Resolvent Operator Technique ◽  
The Resolvent Operator ◽  
Cocoercive Operator ◽  
Cocoercive Operators ◽  
Convergence Of Iterative Algorithm ◽  
New System

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.

scholarly journals Completely generalized multivalued nonlinear quasi-variational inclusions

2002 ◽  
Vol 30 (10) ◽  
pp. 593-604 ◽  
Author(s):  
Zeqing Liu ◽  
Lokenath Debnath ◽  
Shin Min Kang ◽  
Jeong Sheok Ume
Keyword(s):  
Existence Theorems ◽  
Maximal Monotone ◽  
Iterative Algorithms ◽  
Monotone Mappings ◽  
Operator Technique ◽  
Variational Inclusions ◽  
New Class ◽  
Convergence Results ◽  
Resolvent Operator Technique ◽  
The Resolvent Operator

We introduce and study a new class of completely generalized multivalued nonlinear quasi-variational inclusions. Using the resolvent operator technique for maximal monotone mappings, we suggest two kinds of iterative algorithms for solving the completely generalized multivalued nonlinear quasi-variational inclusions. We establish both four existence theorems of solutions for the class of completely generalized multivalued nonlinear quasi-variational inclusions involving strongly monotone, relaxed Lipschitz, and generalized pseudocontractive mappings, and obtain a few convergence results of iterative sequences generated by the algorithms. The results presented in this paper extend, improve, and unify a lot of results due to Adly, Huang, Jou-Yao, Kazmi, Noor, Noor-Al-Said, Noor-Noor, Noor-Noor-Rassias, Shim-Kang-Huang-Cho, Siddiqi-Ansari, Verma, Yao, and Zhang.

scholarly journals Resolvent operator technique for solving a system of generalized variational-like inclusions in Banach spaces

Filomat ◽  
2012 ◽  
Vol 26 (5) ◽  
pp. 897-908
Author(s):  
Rais Ahmad ◽  
Mohammad Dilshad ◽  
Mohammad Akram
Keyword(s):  
Banach Spaces ◽  
Iterative Algorithm ◽  
Resolvent Operator ◽  
Existence Of Solutions ◽  
Operator Technique ◽  
Uniformly Smooth ◽  
Resolvent Operator Technique ◽  
Uniformly Smooth Banach Spaces ◽  
Matlab Programming ◽  
Cocoercive Operator

In this paper, we apply H(?,?)-?-cocoercive operator introduced in [2] for solving a system of generalized variational-like inclusions in q-uniformly smooth Banach spaces. By using the approach of resolvent operator associated with H(?,?)-?-cocoercive operator, an iterative algorithm for solving a system of generalized variational-like inclusions is constructed. We prove the existence of solutions of system of generalized variational-like inclusions and convergence of iterative sequences generated by the algorithm. An example through Matlab programming is constructed.

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

2012 ◽  
Vol 20 (3) ◽  
pp. 131-139
Author(s):  
Shuyi Zhang ◽  
Xinqi Guo ◽  
Dan Luan
Keyword(s):  
Variational Inequality ◽  
Hilbert Spaces ◽  
Resolvent Operator ◽  
Iterative Algorithms ◽  
Operator Technique ◽  
Mixed Variational Inequality ◽  
Generalized System ◽  
Resolvent Operator Technique ◽  
Mixed Variational Inequalities ◽  
The Resolvent Operator

Abstract 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].

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