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

Monther R. Alfuraidan and Mohamed A. Khamsi
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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

Mathematics, 2020, vol. 8, issue 3, 1-6

Abstract: In this work, we investigate the modular version of the Ekeland variational principle (EVP) in the context of variable exponent sequence spaces ? 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 ? p ( · ) .

Keywords: Caristi; Ekeland Variational Principle; Electrorheological fluids; fixed point; modular vector spaces; Nakano; variable exponent sequence spaces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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