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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Bibliographische Detailangaben
Veröffentlicht in:	Advances in difference equations 2020-07, Vol.2020 (1), p.1-11, Article 333
Hauptverfasser:	Khan, Shahid, Adil Khan, Muhammad, Butt, Saad Ihsan, Chu, Yu-Ming
Format:	Artikel
Sprache:	eng
Schlagworte:	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
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Zusammenfassung:	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.
ISSN:	1687-1847 1687-1839 1687-1847
DOI:	10.1186/s13662-020-02794-8