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Halpern-Type Iterative Algorithm for an Infinite Family of Relatively Quasi-Nonexpansive Multivalued Mappings and Equilibrium Problem in Banach Spaces

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Abstract

In this paper, we introduce Halpern-type iterative algorithm for finding a common element of the set of common fixed points of an infinite family of relatively quasi-nonexpansive multivalued mappings and the set of solutions of an equilibrium problem in uniformly smooth and uniformly convex Banach spaces. Strong convergence to common elements of two set is established. Our results improved and extend the corresponding results announced by many others.

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Authors and Affiliations

  1. Department of Mathematics, Mazandaran University of Science and Technology, Behshahr, Iran

    Mohammad Eslamian

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  1. Mohammad Eslamian
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Eslamian, M. Halpern-Type Iterative Algorithm for an Infinite Family of Relatively Quasi-Nonexpansive Multivalued Mappings and Equilibrium Problem in Banach Spaces. Mediterr. J. Math. 11, 713–727 (2014). https://doi.org/10.1007/s00009-013-0330-9

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  • DOI: https://doi.org/10.1007/s00009-013-0330-9

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