A new bound for the Jensen gap pertaining twice differentiable functions with applications

In this paper, we present a new bound for the Jensen gap with the help of a Green function. Using the bound, we deduce a converse of the Hölder inequality as well. Finally, we present some applications of the main result in information theory.

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Podrobná bibliografie
Vydáno v:	Advances in difference equations Ročník 2020; číslo 1; s. 1 - 11
Hlavní autoři:	Khan, Shahid, Adil Khan, Muhammad, Butt, Saad Ihsan, Chu, Yu-Ming
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Cham Springer International Publishing 06.07.2020 Springer Nature B.V SpringerOpen
Témata:	Analysis Applications Convex function Csiszár divergence Difference and Functional Equations Functional Analysis Green function Green's functions Hölder inequality Information theory Jensen inequality Mathematics Mathematics and Statistics Methods Ordinary Differential Equations Partial Differential Equations Topics in Special Functions and q-Special Functions: Theory Csiszár divergence 26A51 Convex function Hölder inequality Jensen inequality Green function 26D15
ISSN:	1687-1847, 1687-1839, 1687-1847
On-line přístup:	Získat plný text
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Popis
Shrnutí:	In this paper, we present a new bound for the Jensen gap with the help of a Green function. Using the bound, we deduce a converse of the Hölder inequality as well. Finally, we present some applications of the main result in information theory.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1687-1847 1687-1839 1687-1847
DOI:	10.1186/s13662-020-02794-8