Fixed points for several classes of mappings in variable Lebesgue spaces. (3rd June 2021)

• Record Type: Journal Article
• Authors: Domínguez Benavides, T.; Moshtaghioun, S. M.; Sadeghi Hafshejani, A.
• Is Part Of: Optimization. Volume 70:Number 5/6(2021)
• Page Start: 911
• Page End: 927
• Publication Date: 2021-06-03
• Subjects: Variable Lebesgue spaces -- fixed point -- uniformly Lipschitz mappings -- asymptotically regular mappings; 47H09 -- 47H10; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1711086
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: The variable Lebesgue spaces are a generalization of the classical Lebesgue spaces, replacing the constant exponent p with a variable exponent function p ( ⋅ ) . 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.