Graph convergence for H(., .)-cocoercive operator in q-uniformly smooth Banach spaces with an application

Faizan Ahmad Khan

Abstract


In this paper, we consider a class of H(., .) -cocoercive operator, which generalizes many existing monotone operators. Further, we introduce a concept of graph convergence concerned with the H(., .)-cocoercive operator in q-uniformly smooth Banach spaces and given an equivalence theorem between graph-convergence and resolvent operator convergence for the H(., .)-cocoercive operator. As an application, a perturbed algorithm for solving a class of variational inclusion involving H(., .)-cocoercive operator is constructed. Furthermore, under some suitable conditions, the existence of the solution for the variational inclusion and the convergence of iterative sequence generated by perturbed algorithm are given.

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How to Cite this Article:

Faizan Ahmad Khan, Graph convergence for H(., .)-cocoercive operator in q-uniformly smooth Banach spaces with an application, Journal of Mathematical and Computational Science, Vol 4, No 6 (2014), 1010-1024

Copyright © 2014 Faizan Ahmad Khan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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