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A Halpern-Mann Type Iteration for Fixed Point Problems of a Relatively Nonexpansive Mapping and a System of Equilibrium Problems

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  • Utith Inprasit
  • Weerayuth Nilsrakoo

Abstract

A new modified Halpern-Mann type iterative method is constructed. Strong convergence of the scheme to a common element of the set of fixed points of a relatively nonexpansive mapping and the set of common solutions to a system of equilibrium problems in a uniformly convex real Banach space which is also uniformly smooth is proved. The results presented in this work improve on the corresponding ones announced by many others.

Suggested Citation

  • Utith Inprasit & Weerayuth Nilsrakoo, 2011. "A Halpern-Mann Type Iteration for Fixed Point Problems of a Relatively Nonexpansive Mapping and a System of Equilibrium Problems," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-22, September.
    • Handle: RePEc:hin:jnlaaa:632857
    DOI: 10.1155/2011/632857
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