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

Alfuraidan, Monther R.; Khamsi, Mohamed A.

doi:10.3390/math8030375

Open AccessArticle

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

by

Monther R. Alfuraidan

¹

and

Mohamed A. Khamsi

^2,*

¹

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

²

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

^*

Author to whom correspondence should be addressed.

Mathematics 2020, 8(3), 375; https://doi.org/10.3390/math8030375

Submission received: 12 February 2020 / Revised: 28 February 2020 / Accepted: 2 March 2020 / Published: 7 March 2020

(This article belongs to the Special Issue Fixed Point, Optimization, and Applications)

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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 (\cdot)}

. 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 (\cdot)}

.

Keywords: Caristi; Ekeland Variational Principle; Electrorheological fluids; fixed point; modular vector spaces; Nakano; variable exponent sequence spaces

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Alfuraidan, M.R.; Khamsi, M.A. Ekeland Variational Principle in the Variable Exponent Sequence Spaces ℓ_p(·). Mathematics 2020, 8, 375. https://doi.org/10.3390/math8030375

AMA Style

Alfuraidan MR, Khamsi MA. Ekeland Variational Principle in the Variable Exponent Sequence Spaces ℓ_p(·). Mathematics. 2020; 8(3):375. https://doi.org/10.3390/math8030375

Chicago/Turabian Style

Alfuraidan, Monther R., and Mohamed A. Khamsi. 2020. "Ekeland Variational Principle in the Variable Exponent Sequence Spaces ℓ_p(·)" Mathematics 8, no. 3: 375. https://doi.org/10.3390/math8030375

APA Style

Alfuraidan, M. R., & Khamsi, M. A. (2020). Ekeland Variational Principle in the Variable Exponent Sequence Spaces ℓ_p(·). Mathematics, 8(3), 375. https://doi.org/10.3390/math8030375

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

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