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Ekeland Variational Principle in the Variable Exponent Sequence Spaces ℓ p (·)

Author

Listed:
  • Monther R. Alfuraidan

    (Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia)

  • Mohamed A. Khamsi

    (Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, TX 79968, USA)

Abstract

In this work, we investigate the modular version of the Ekeland variational principle (EVP) in the context of variable exponent sequence spaces ℓ p ( · ) . The core obstacle in the development of a modular version of the EVP is the failure of the triangle inequality for the module. It is the lack of this inequality, which is indispensable in the establishment of the classical EVP, that has hitherto prevented a successful treatment of the modular case. As an application, we establish a modular version of Caristi’s fixed point theorem in ℓ p ( · ) .

Suggested Citation

  • Monther R. Alfuraidan & Mohamed A. Khamsi, 2020. "Ekeland Variational Principle in the Variable Exponent Sequence Spaces ℓ p (·)," Mathematics, MDPI, vol. 8(3), pages 1-6, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:375-:d:329813
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