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An Iterative Method for a Common Solution of Split Generalized Equilibrium Problems and Fixed Points of a Finite Family of Nonexpansive Mapping

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Nonlinear Analysis and Global Optimization

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 167))

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Abstract

In this paper, we introduce and analyze a general iterative algorithm for finding an approximate element of the common set of solutions of the split generalized equilibrium problem and the set of common fixed points of a finite family of nonexpansive mapping in the setting of real Hilbert space. Under appropriate conditions, we derive the strong convergence results for this method. Preliminary numerical experiments are included to verify the theoretical assertions of the proposed method. The results presented in this paper extend and improve some well-known results in the literature.

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Author information

Authors and Affiliations

  1. Equipe MAISI, Ibn Zohr University, ENSA, Agadir, Morocco

    Ihssane Hay & Abdellah Bnouhachem

  2. Department of Mathematics, National Technical University of Athens Zografou Campus, Athens, Greece

    Themistocles M. Rassias

Authors
  1. Ihssane Hay
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  2. Abdellah Bnouhachem
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  3. Themistocles M. Rassias
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Editor information

Editors and Affiliations

  1. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

  2. Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

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Hay, I., Bnouhachem, A., Rassias, T.M. (2021). An Iterative Method for a Common Solution of Split Generalized Equilibrium Problems and Fixed Points of a Finite Family of Nonexpansive Mapping. In: Rassias, T.M., Pardalos, P.M. (eds) Nonlinear Analysis and Global Optimization. Springer Optimization and Its Applications, vol 167. Springer, Cham. https://doi.org/10.1007/978-3-030-61732-5_10

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