A new hybrid projection algorithm for system of equilibrium problems and variational inequality problems and two finite families of quasi-φ- nonexpansive mappings

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POOM KUMAM

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Publication Details

Author list: Phuangphoo P., Kumam P.

Publisher: Hindawi

Publication year: 2013

Journal: Abstract and Applied Analysis (1085-3375)

Volume number: 2013

ISSN: 1085-3375

eISSN: 1687-0409

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84874825811&doi=10.1155%2f2013%2f107296&partnerID=40&md5=b7707a6bb25772b1f764a24fbd9de9d7

Languages: English-Great Britain (EN-GB)

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Abstract

We introduce a modified Mann's iterative procedure by using the hybrid projection method for solving the common solution of the system of equilibrium problems for a finite family of bifunctions satisfying certain condition, the common solution of fixed point problems for two finite families of quasi-φ-nonexpansive mappings, and the common solution of variational inequality problems for a finite family of continuous monotone mappings in a uniformly smooth and strictly convex real Banach space. Then, we prove a strong convergence theorem of the iterative procedure generated by some mild conditions. Our result presented in this paper improves and generalizes some well-known results in the literature. © 2013 Pongrus Phuangphoo and Poom Kumam.

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