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Levitin–Polyak well-posedness for split equilibrium problems

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

The notion of well-posedness has drawn the attention of many researchers in the field of nonlinear analysis, as it allows to explore problems in which exact solutions are not known and/or computationally hard to compute. Roughly speaking, for a given problem, well-posedness guarantees the convergence of approximations to exact solutions via an iterative method. Thus, in this paper we extend the concept of Levitin–Polyak well-posedness to split equilibrium problems in real Banach spaces. In particular, we establish a metric characterization of Levitin–Polyak well-posedness by perturbations and also show an equivalence between Levitin–Polyak well-posedness by perturbations for split equilibrium problems and the existence and uniqueness of their solutions.

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Acknowledgements

The first author gratefully acknowledges the financial support of the Post-Doctoral Program at the Technion-Israel Institute of Technology. Simeon Reich was partially supported by the Israel Science Foundation (Grant 820/17), by the Fund for the Promotion of Research at the Technion and by the Technion General Research Fund. All the authors are grateful to the editor and to two anonymous referees for their useful comments and helpful suggestions.

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Authors and Affiliations

  1. Department of Mathematics, The Technion-Israel Institute of Technology, 3200003, Haifa, Israel

    Soumitra Dey & Simeon Reich

  2. Department of Mathematics, Braude College, 2161002, Karmiel, Israel

    Aviv Gibali

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  1. Soumitra Dey
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  2. Aviv Gibali
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  3. Simeon Reich
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Correspondence to Soumitra Dey, Aviv Gibali or Simeon Reich.

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Dey, S., Gibali, A. & Reich, S. Levitin–Polyak well-posedness for split equilibrium problems. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 117, 88 (2023). https://doi.org/10.1007/s13398-023-01416-8

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  • DOI: https://doi.org/10.1007/s13398-023-01416-8

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