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Modified viscosity implicit rules for nonexpansive mappings in Hilbert spaces

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Abstract

In this paper, we study a modified viscosity implicit rule of a nonexpansive mapping in Hilbert spaces. Strong convergence theorems are obtained under some suitable assumptions imposed on the parameters. As applications, we obtain some strong convergence theorems for solving fixed-point problems of strict pseudocontractive mappings and finite equilibrium problems in Hilbert spaces. We also give some numerical examples to support our main 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, Wisconsin, 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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Corresponding author

Correspondence to Gang Cai.

Additional information

This work was supported by the NSF of China (No. 11401063), the University Young Core Teacher Foundation of Chongqing (020603011714), and Science and Technology Project of Chongqing Education Committee (Grant No. KJ1500313, KJ KJ1703041, KJ1703043).

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Cai, G., Shehu, Y. & Iyiola, O.S. Modified viscosity implicit rules for nonexpansive mappings in Hilbert spaces. J. Fixed Point Theory Appl. 19, 2831–2846 (2017). https://doi.org/10.1007/s11784-017-0458-5

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  • DOI: https://doi.org/10.1007/s11784-017-0458-5

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