Generalized -Cocoercive Operators and Generalized Set-Valued Variational-Like Inclusions

Shamshad Husain, Sanjeev Gupta and Vishnu Narayan Mishra

Journal of Mathematics, 2013, vol. 2013, 1-10

Abstract:

We investigate a new class of cocoercive operators named generalized -cocoercive operators in Hilbert spaces. We prove that generalized -cocoercive operator is single-valued and Lipschitz continuous and extends the concept of resolvent operators associated with -cocoercive operators to the generalized -cocoercive operators. Some examples are given to justify the definition of generalized -cocoercive operators. Further, we consider a generalized set-valued variational-like inclusion problem involving generalized -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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:738491

DOI: 10.1155/2013/738491

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