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Viscosity iterative algorithms for fixed point problems of asymptotically nonexpansive mappings in the intermediate sense and variational inequality problems in Banach spaces

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Abstract

In this paper, we introduce a generalized viscosity algorithm for finding a fixed point of an asymptotically nonexpansive mapping in the intermediate sense which is also a solution to a variational inequality problem of two inverse-strongly monotone operators in 2-uniformly smooth and uniformly convex Banach spaces. Strong convergence theorems are given under suitable assumptions imposed on the parameters. The results obtained in this paper improve and extend many recent ones in the literature. Three numerical examples are also given to show the efficiency and implementation of our results.

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Authors and Affiliations

  1. School of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, China

    Gang Cai

  2. Department of Mathematics, University of Nigeria, Nsukka, Nigeria

    Yekini Shehu

  3. Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI, USA

    Olaniyi Samuel Iyiola

Authors
  1. Gang Cai
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  2. Yekini Shehu
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  3. Olaniyi Samuel Iyiola
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Correspondence to Gang Cai.

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Cai, G., Shehu, Y. & Iyiola, O.S. Viscosity iterative algorithms for fixed point problems of asymptotically nonexpansive mappings in the intermediate sense and variational inequality problems in Banach spaces. Numer Algor 76, 521–553 (2017). https://doi.org/10.1007/s11075-017-0269-1

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  • DOI: https://doi.org/10.1007/s11075-017-0269-1

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