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Strong convergence theorems for approximating common fixed points of families of nonexpansive mappings and applications

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Abstract

An implicit algorithm for finding common fixed points of an uncountable family of nonexpansive mappings is proposed. A new inexact iteration method is also proposed for countable family of nonexpansive mappings. Several strong convergence theorems based on our main results are established in the setting of Banach spaces. Both algorithms are applied for finding zeros of accretive operators and for solving convex minimization, split feasibility and equilibrium problems.

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Authors and Affiliations

  1. Department of Mathematics, Banaras Hindu University, Varanasi, 221005, India

    D. R. Sahu

  2. Dipartimento di Matematica, Universita della Calabria, 87036, Arcavacata di Rende (Cs), Italy

    V. Colao & G. Marino

Authors
  1. D. R. Sahu
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  2. V. Colao
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  3. G. Marino
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Correspondence to G. Marino.

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Sahu, D.R., Colao, V. & Marino, G. Strong convergence theorems for approximating common fixed points of families of nonexpansive mappings and applications. J Glob Optim 56, 1631–1651 (2013). https://doi.org/10.1007/s10898-012-9929-9

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  • DOI: https://doi.org/10.1007/s10898-012-9929-9

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