Viscosity approximation methods of random fixed point solutions and random variational inequalities in Hilbert spaces

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Publication Details

Author list: Kumam P., Plubtieng S.

Publisher: World Scientific Publishing

Publication year: 2011

Journal: Asian-European Journal of Mathematics (1793-5571)

Volume number: 4

Issue number: 2

Start page: 283

End page: 293

Number of pages: 11

ISSN: 1793-5571

eISSN: 1793-7183

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84857546523&doi=10.1142%2fS1793557111000228&partnerID=40&md5=e10fab5f6b02bfaf357e5cbf34cb4d1b

Languages: English-Great Britain (EN-GB)

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Abstract

In this paper, we construct random iterative processes for nonexpansive random operators and study necessary conditions for these processes. It is shown that these random iterative processes converge to random fixed points of nonexpansive random operators and solve some random variational inequalities. We also proved that an implicit random iterative process converges to the random fixed point and solves these random variational inequalities. Our results can be viewed as a refinement and improvement of the previously known results for variational inequality theory and also give generalization stochastic version of some results of Xu [23]. ฉ 2011 World Scientific Publishing Company.

Keywords

measurable spaces, nonexpansive random operator, random variational inequalities