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Iterative algorithms for solving variational inequalities and fixed point problems for asymptotically nonexpansive mappings in Banach spaces

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Abstract

The purpose of this paper is to study some iterative algorithms for finding a common element of the set of solutions of systems of variational inequalities for inverse-strongly accretive mappings and the set of fixed points of an asymptotically nonexpansive mapping in uniformly convex and 2-uniformly smooth Banach space or uniformly convex and q-uniformly smooth Banach space. Strong convergence theorems are obtained under suitable conditions. We also give some numerical examples to support our main results. The results obtained in this paper improve and extend the recent ones announced by many others in the literature.

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Authors and Affiliations

  1. School of Mathematics Science, 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. Iterative algorithms for solving variational inequalities and fixed point problems for asymptotically nonexpansive mappings in Banach spaces. Numer Algor 73, 869–906 (2016). https://doi.org/10.1007/s11075-016-0121-z

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  • DOI: https://doi.org/10.1007/s11075-016-0121-z

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