A new general system of generalized nonlinear mixed composite-type equilibria and fixed point problems with an application to minimization problems

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POOM KUMAM

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Publication Details

Author list: Sunthrayuth P., Kumam P.

Publisher: Hindawi

Publication year: 2012

Journal: Abstract and Applied Analysis (1085-3375)

Volume number: 2012

ISSN: 1085-3375

eISSN: 1687-0409

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84871462633&doi=10.1155%2f2012%2f414718&partnerID=40&md5=0dd690fee9136d71c6d45914101b6bd5

Languages: English-Great Britain (EN-GB)

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Abstract

We introduce a new general system of generalized nonlinear mixed composite-type equilibria and propose a new iterative scheme for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of a general system of generalized nonlinear mixed composite-type equilibria, and the set of fixed points of a countable family of strict pseudocontraction mappings. Furthermore, we prove the strong convergence theorem of the purposed iterative scheme in a real Hilbert space. As applications, we apply our results to solve a certain minimization problem related to a strongly positive bounded linear operator. Finally, we also give a numerical example which supports our results. The results obtained in this paper extend the recent ones announced by many others. ฉ 2012 Pongsakorn Sunthrayuth and Poom Kumam.

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