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

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  • D. Sahu
  • V. Colao
  • G. Marino

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. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • D. Sahu & V. Colao & G. Marino, 2013. "Strong convergence theorems for approximating common fixed points of families of nonexpansive mappings and applications," Journal of Global Optimization, Springer, vol. 56(4), pages 1631-1651, August.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:4:p:1631-1651
    DOI: 10.1007/s10898-012-9929-9
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    References listed on IDEAS

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    1. D. Sahu & J. Yao, 2011. "The prox-Tikhonov regularization method for the proximal point algorithm in Banach spaces," Journal of Global Optimization, Springer, vol. 51(4), pages 641-655, December.
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