\(H(.,.)-\eta\)-cocoercive operators and variational-like inclusions in Banach spaces
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Authors
Rais Ahmad
- Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India.
Mohammad Dilshad
- Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India.
Abstract
In this paper, we define \(H(.,.)-\eta\)-cocoercive operators in q-uniformly smooth Banach spaces and its resolvent
operator. We prove the Lipschitz continuity of the resolvent operator associated with \(H(.,.)-\eta\)-cocoercive
operator and estimate its Lipschitz constant. By using the techniques of resolvent operator, an iterative
algorithm for solving a variational-like inclusion problem is constructed. The existence of solution for the
variational-like inclusions and the convergence of iterative sequences generated by the algorithm is proved.
Some examples are given.
Share and Cite
ISRP Style
Rais Ahmad, Mohammad Dilshad, \(H(.,.)-\eta\)-cocoercive operators and variational-like inclusions in Banach spaces, Journal of Nonlinear Sciences and Applications, 5 (2012), no. 5, 334--344
AMA Style
Ahmad Rais, Dilshad Mohammad, \(H(.,.)-\eta\)-cocoercive operators and variational-like inclusions in Banach spaces. J. Nonlinear Sci. Appl. (2012); 5(5):334--344
Chicago/Turabian Style
Ahmad, Rais, Dilshad, Mohammad. "\(H(.,.)-\eta\)-cocoercive operators and variational-like inclusions in Banach spaces." Journal of Nonlinear Sciences and Applications, 5, no. 5 (2012): 334--344
Keywords
- \(H(.
- .)-\eta\)-cocoercive
- Algorithm
- Inclusion
- Banach spaces
- Lipschitz continuity.
MSC
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