scholarly journals -Mixed Cocoercive Operators with an Application for Solving Variational Inclusions in Hilbert Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Shamshad Husain ◽  
Sanjeev Gupta
Keyword(s):  
Hilbert Spaces ◽  
Variational Inclusions ◽  
Cocoercive Operators

scholarly journals Algorithm for Solving a New System of Generalized Variational Inclusions in Hilbert Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Shamshad Husain ◽  
Sanjeev Gupta
Keyword(s):  
Variational Inequalities ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Existence Of Solutions ◽  
Variational Inclusions ◽  
Special Cases ◽  
Systems Of Variational Inequalities ◽  
Cocoercive Operators ◽  
New System

We introduce and study a new system of generalized variational inclusions involving -cocoercive and relaxed -cocoercive operators, which contain the systems of variational inclusions and the systems of variational inequalities, variational inclusions, and variational inequalities as special cases. By using the resolvent technique for the -cocoercive operators, we prove the existence of solutions and the convergence of a new iterative algorithm for this system of variational inclusions in Hilbert spaces. An example is given to justify the main result. Our results can be viewed as a generalization of some known results in the literature.

scholarly journals On a System of Nonlinear Variational Inclusions withHh,η-Monotone Operators

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Zeqing Liu ◽  
Jeong Sheok Ume ◽  
Shin Min Kang
Keyword(s):  
Hilbert Spaces ◽  
Monotone Operators ◽  
Variational Inclusions ◽  
Iterative Approximation

This paper is concerned mainly with the existence and iterative approximation of solutions for a system of nonlinear variational inclusions involving the stronglyHh,η-monotone operators in Hilbert spaces. The results presented in this paper extend, improve, and unify many known results in the literature.

scholarly journals Generalized Nonlinear Variational Inclusions Involving (A,η)-Monotone Mappings in Hilbert Spaces

2007 ◽  
Vol 2007 ◽  
pp. 1-6 ◽  
Author(s):  
Yeol Je Cho ◽  
Xiaolong Qin ◽  
Meijuan Shang ◽  
Yongfu Su
Keyword(s):  
Hilbert Spaces ◽  
Monotone Mappings ◽  
Variational Inclusions

scholarly journals Sensitivity Analysis for a System of Generalized Nonlinear Mixed Quasi Variational Inclusions withH-Monotone Operators

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Han-Wen Cao
Keyword(s):  
Sensitivity Analysis ◽  
Hilbert Spaces ◽  
Monotone Operators ◽  
Variational Inclusions ◽  
New System

The existence of the solution for a new system of generalized nonlinear mixed quasi variational inclusions withH-monotone operators is proved by using implicit resolvent technique, and the sensitivity analysis of solution in Hilbert spaces is given. Our results improve and generalize some results of the recent ones.

scholarly journals A new system of variational inclusions with (H, η)-monotone operators

2006 ◽  
Vol 74 (2) ◽  
pp. 301-319 ◽  
Author(s):  
Jianwen Peng ◽  
Jianrong Huang
Keyword(s):  
Hilbert Spaces ◽  
Resolvent Operator ◽  
Iterative Algorithms ◽  
Operator Method ◽  
Monotone Operators ◽  
Variational Inclusions ◽  
Uniqueness Of Solutions ◽  
Special Cases ◽  
The Resolvent Operator ◽  
New System

In this paper, We introduce and study a new system of variational inclusions involving(H, η)-monotone operators in Hilbert spaces. By using the resolvent operator method associated with (H, η)-monotone operators, we prove the existence and uniqueness of solutions and the convergence of some new three-step iterative algorithms for this system of variational inclusions and its special cases. The results in this paper extends and improves some results in the literature.

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