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Krasnoselski-Mann Iterations for Hierarchical Fixed Point Problems for a Finite Family of Nonself Mappings in Banach Spaces

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Abstract

This paper deals with a method for approximating a solution of the following problem: find hierarchically a common fixed point of a finite family of nonself nonexpansive mappings with respect to a nonexpansive self mapping on a closed convex subset of a smooth and reflexive Banach space X, which admits a weakly sequentially continuous duality mapping. First, we prove a weak convergence theorem which extends and improves one recent result proved by Yao and Liou (see Inverse Problems 24 (2008), doi:10.1088/0266-5611/24/1/015015). Secondly, when the self mapping is a contraction, we prove, under different restrictions on parameters, a strong convergence result which generalize some recent results in the literature.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China

    L. C. Ceng

  2. Department of Mathematics, Babeş-Bolyai University Cluj-Napoca, 400084, Cluj-Napoca, Romania

    A. Petruşel

Authors
  1. L. C. Ceng
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  2. A. Petruşel
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Correspondence to A. Petruşel.

Additional information

Communicated by J.C. Yao.

L.C. Ceng research was partially supported by the National Science Foundation of China (10771141), Ph.D. Program Foundation of Ministry of Education of China (20070270004) and Science and Technology Commission of Shanghai Municipality grant (075105118).

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Ceng, L.C., Petruşel, A. Krasnoselski-Mann Iterations for Hierarchical Fixed Point Problems for a Finite Family of Nonself Mappings in Banach Spaces. J Optim Theory Appl 146, 617–639 (2010). https://doi.org/10.1007/s10957-010-9679-0

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