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Approximation of common fixed points of asymptotically nonexpansive cosine family based on modified Ishikawa iterations

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Abstract

In this paper a modified Ishikawa iterative process for approximating a common fixed point of a locally asymptotically nonexpansive cosine family is firstly introduced, and then, by using the theory of cosine families and constructing some control conditions, several strong convergence theorems are established for this iterative process in Banach spaces. Moreover, an example is presented to illustrate the main result of the paper.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, 210044, People’s Republic of China

    Jian-Zhong Xiao

  2. School of Computer and Software, Nanjing University of Information Science and Technology, Nanjing, 210044, People’s Republic of China

    Yue Zhu

Authors
  1. Jian-Zhong Xiao
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  2. Yue Zhu
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Correspondence to Jian-Zhong Xiao.

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Communicated by Eduardo Souza de Cursi.

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This work was supported by the National Natural Science Foundation of China (Grant nos. 11571176, 111701289).

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Xiao, JZ., Zhu, Y. Approximation of common fixed points of asymptotically nonexpansive cosine family based on modified Ishikawa iterations. Comp. Appl. Math. 38, 151 (2019). https://doi.org/10.1007/s40314-019-0932-3

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  • DOI: https://doi.org/10.1007/s40314-019-0932-3

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