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Convergence of an iterative method for relatively nonexpansive multi-valued mappings and equilibrium problems in Banach spaces

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Abstract

In this paper, an iterative sequence for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of two relatively nonexpansive multi-valued mappings is introduced. This iterative scheme can be viewed as a multi-valued version of the corresponding one introduced by Zhang et al. (Comput Math Appl 61, 262–276, 2011) for two relatively nonexpansive multi-valued mappings. Finally, strong convergence of this sequence is studied in Banach spaces.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Imam Khomeini International University, P. O. Box 34149-16818, Qazvin, Iran

    S. Homaeipour & A. Razani

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  1. S. Homaeipour
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  2. A. Razani
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Correspondence to S. Homaeipour.

Additional information

A. Razani would like to thank Imam Khomeini International University, for supporting this research (Grant No. 751168-91)

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Homaeipour, S., Razani, A. Convergence of an iterative method for relatively nonexpansive multi-valued mappings and equilibrium problems in Banach spaces. Optim Lett 8, 211–225 (2014). https://doi.org/10.1007/s11590-012-0562-9

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  • DOI: https://doi.org/10.1007/s11590-012-0562-9

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