scholarly journals A Wiener-Hopf Dynamical System for Mixed Equilibrium Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Farhat Suhel ◽  
S. K. Srivastava ◽  
Suhel Ahmad Khan
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Asymptotic Property ◽  
Resolvent Operator ◽  
Equilibrium Problems ◽  
Operator Technique ◽  
Mixed Equilibrium Problems ◽  
Resolvent Operator Technique ◽  
Mixed Equilibrium ◽  
The Resolvent Operator

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.

scholarly journals On Mixed Equilibrium Problems in Hadamard Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Chinedu Izuchukwu ◽  
Kazeem Olalekan Aremu ◽  
Olawale Kazeem Oyewole ◽  
Oluwatosin Temitope Mewomo ◽  
Safeer Hussain Khan
Keyword(s):  
Equilibrium Problem ◽  
Resolvent Operator ◽  
Equilibrium Problems ◽  
Existence Of Solution ◽  
Mixed Equilibrium Problem ◽  
Proximal Point ◽  
Unique Existence ◽  
Mixed Equilibrium Problems ◽  
Mixed Equilibrium ◽  
The Resolvent Operator

The main purpose of this paper is to study mixed equilibrium problems in Hadamard spaces. First, we establish the existence of solution of the mixed equilibrium problem and the unique existence of the resolvent operator for the problem. We then prove a strong convergence of the resolvent and a Δ-convergence of the proximal point algorithm to a solution of the mixed equilibrium problem under some suitable conditions. Furthermore, we study the asymptotic behavior of the sequence generated by a Halpern-type PPA. Finally, we give a numerical example in a nonlinear space setting to illustrate the applicability of our results. Our results extend and unify some related results in the literature.

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 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 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 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 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].

The effect of collisions on the coherent scattering from strongly driven two level atoms

1981 ◽  
Vol 59 (8) ◽  
pp. 990-993
Author(s):  
H. R. Zaidi ◽  
Mahendra Prasad
Keyword(s):  
Resolvent Operator ◽  
Strong Field ◽  
Coherent Scattering ◽  
Function Technique ◽  
Operator Technique ◽  
Field Region ◽  
Collisional Relaxation ◽  
Liouville Space ◽  
Resolvent Operator Technique ◽  
The Resolvent Operator

The existence of a coherent mode in phase with the near resonant driving field is reconsidered using the resolvent operator technique in Liouville space. A result, previously obtained from Green function technique, is rederived. It is shown that such a mode does not exist in the general case of collisional relaxation in a gas. As a result, the coherent scattering component acquires a nonzero width in the strong field region. This width depends on some non-Markovian collision parameters.

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.

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