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The modified viscosity implicit rules for variational inequality problems and fixed point problems of nonexpansive mappings in Hilbert spaces

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Abstract

The purpose of this paper is to introduce a modified viscosity implicit rules for finding a common element of the set of solutions of variational inequality problems for two inverse-strongly monotone operators and the set of fixed points of one nonexpansive mapping in Hilbert spaces. Under some suitable assumptions imposed on the parameters, we obtain some strong convergence theorems. We also apply our main results to solve fixed point problems for strict pseudocontractive mappings and equilibrium problems in Hilbert spaces. A numerical example is given for supporting 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, Zhejiang Normal University, Zhejiang, 321004, China

    Yekini Shehu

  3. California University of Pennsylvania, California, PA, 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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This work was supported by the NSF of China (Grant nos. 11401063, 11771063), the Natural Science Foundation of Chongqing (Grant nos. cstc2017jcyjAX0006, KJZDM201800501), Science and Technology Project of Chongqing Education Committee (Grant no. KJ1703041), the University Young Core Teacher Foundation of Chongqing (Grant no. 020603011714), Talent Project of Chongqing Normal University (Grant no. 02030307-00024).

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Cai, G., Shehu, Y. & Iyiola, O.S. The modified viscosity implicit rules for variational inequality problems and fixed point problems of nonexpansive mappings in Hilbert spaces. RACSAM 113, 3545–3562 (2019). https://doi.org/10.1007/s13398-019-00716-2

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  • DOI: https://doi.org/10.1007/s13398-019-00716-2

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