Fixed points for several classes of mappings in variable Lebesgue spaces

ABSTRACT

The variable Lebesgue spaces are a generalization of the classical Lebesgue spaces, replacing the constant exponent p with a variable exponent function $p(\cdot )$. Beside their intrinsic interest, they are also very important for their applications to partial differential equations and variational integrals with non-standard growth conditions. In this paper, we study some properties related to the existence of a fixed point for several classes of mappings defined on these spaces, considering both the modular and its induced norm.

KEYWORDS:

• Variable Lebesgue spaces
• fixed point
• uniformly Lipschitz mappings
• asymptotically regular mappings

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 47H09
• 47H10

Disclosure statement

No potential conflict of interest was reported by the authors.

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

The first author is partially supported by MINECO [grant number PGC2018-098474-B-C21] and Andalusian Regional Government [grant number FQM-127].