Ekeland variational principle in the variable exponent sequence spaces lp(·)

Monther R. Alfuraidan; Mohamed A. Khamsi

doi:10.3390/math8030375

Ekeland variational principle in the variable exponent sequence spaces l_p(·)

Monther R. Alfuraidan
, Mohamed A. Khamsi^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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(·).

Original language	English
Article number	375
Journal	Mathematics
Volume	8
Issue number	3
DOIs	https://doi.org/10.3390/math8030375
State	Published - 1 Mar 2020

Bibliographical note

Publisher Copyright:
© 2020 by the authors. Licensee MDPI, Basel, Switzerland.

Keywords

Caristi
Ekeland variational principle
Electrorheological fluids
Fixed point
Modular vector spaces
Nakano
Variable exponent sequence spaces

ASJC Scopus subject areas

General Mathematics

Access to Document

10.3390/math8030375

Cite this

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