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 ( · ) .
Highlights
The variable exponent sequence spaces can be traced back to the seminal work by W
As a byproduct of our result, we present a modular version of the Caristi fixed point theorem
The modular version of Ekeland variational principle (EVP) was difficult to establish because the modular fails the triangle inequality, which is indispensable in the establishment of EVP in metric spaces
Summary
The variable exponent sequence spaces can be traced back to the seminal work by W. The variable exponent sequence spaces were thoroughly examined by many, among others: [2,3,4,5,6]. As a byproduct of our result, we present a modular version of the Caristi fixed point theorem.
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