IJAM: Volume 37, No. 3 (2024)

DOI: 10.12732/ijam.v37i3.6

PROPERTIES OF THE UNIFORM

CONVEXITY AND UNIFORM

SMOOTHNESS OF VARIABLE

EXPONENT LEBESGUE SPACES

Mykola Yaremenko

Physico-Mathematical Department

The National Technical University of Ukraine

“Igor Sikorsky Kyiv Polytechnic Institute”

37, Prospect Beresteiskyi (former Peremohy)

Kyiv – 03056, UKRAINE

Abstract. We consider the uniform convexity of variable exponent Lebesgue spaces. We establish that for all $\varepsilon \in (0,2)$ and all unit vectors $u, v \in L^{p(.)}$ such that

$||u-v|| _ L^{p(.)}$ we can take numbers $\delta(\varepsilon) = … $ if …. and …. so that ….

A uniform convexity of variable Lebesgue space $ L^{p(.)}$ is proven. Some correlations for functions describing uniform convexity and uniform smoothness of spaces $ L^{p(.)}$ were established.

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How to cite this paper?
DOI: 10.12732/ijam.v37i3.6
Source: International Journal of Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 2024
Volume: 37
Issue: 3

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IJAM: Volume 37, No. 3 (2024)

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