Generalized H(·,·,·)-η-Cocoercive Operators and Generalized Set-Valued Variational-Like Inclusions
Joint Authors
Husain, Shamshad
Mishra, Vishnu Narayan
Gupta, Sanjeev
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-06-13
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
We investigate a new class of cocoercive operators named generalized H(·,·,·)-η-cocoercive operators in Hilbert spaces.
We prove that generalized H(·,·,·)-η-cocoercive operator is single-valued and Lipschitz continuous and extends the concept of resolvent operators associated with H(·,·)-cocoercive operators to the generalized H(·,·,·)-η-cocoercive operators.
Some examples are given to justify the definition of generalized H(·,·,·)-η-cocoercive operators.
Further, we consider a generalized set-valued variational-like inclusion problem involving generalized H(·,·,·)-η-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.
American Psychological Association (APA)
Husain, Shamshad& Gupta, Sanjeev& Mishra, Vishnu Narayan. 2013. Generalized H(·,·,·)-η-Cocoercive Operators and Generalized Set-Valued Variational-Like Inclusions. Journal of Mathematics،Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-494777
Modern Language Association (MLA)
Husain, Shamshad…[et al.]. Generalized H(·,·,·)-η-Cocoercive Operators and Generalized Set-Valued Variational-Like Inclusions. Journal of Mathematics No. 2013 (2013), pp.1-10.
https://search.emarefa.net/detail/BIM-494777
American Medical Association (AMA)
Husain, Shamshad& Gupta, Sanjeev& Mishra, Vishnu Narayan. Generalized H(·,·,·)-η-Cocoercive Operators and Generalized Set-Valued Variational-Like Inclusions. Journal of Mathematics. 2013. Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-494777
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-494777