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Viscosity Approximation Methods for Zeros of Accretive Operators and Fixed Point Problems in Banach Spaces

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Abstract

In this paper, we introduce iterative algorithms for finding a zero of set-valued accretive operators by the viscosity approximation method based on Meir–Keeler-type contractions in a reflexive Banach space which admits a weakly continuous duality mapping. We obtain some strong convergence theorems under suitable conditions. As applications, we apply our results for finding common fixed point of nonexpansive semigroups and for solving equilibrium problem, optimization problem, and variational inequalities.

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Acknowledgments

This work was supported by the Higher Education Research Promotion and National Research University Project of Thailand , Office of the Higher Education Commission (NRU-CSEC No. 57000621).

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bang Mod, Thrung Khru, Bangkok, 10140, Thailand

    Pongsakorn Sunthrayuth & Poom Kumam

  2. Department of Mathematics Education and the RINS, Gyeongsang National University, Jinju, 660-701, Republic of Korea

    Yeol Je Cho

Authors
  1. Pongsakorn Sunthrayuth
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  2. Yeol Je Cho
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  3. Poom Kumam
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Correspondence to Pongsakorn Sunthrayuth.

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Communicated by Mohammad Sal Mosleihan.

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Sunthrayuth, P., Cho, Y.J. & Kumam, P. Viscosity Approximation Methods for Zeros of Accretive Operators and Fixed Point Problems in Banach Spaces. Bull. Malays. Math. Sci. Soc. 39, 773–793 (2016). https://doi.org/10.1007/s40840-015-0139-8

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  • DOI: https://doi.org/10.1007/s40840-015-0139-8

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