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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Bibliographic Details
Published in:Advances in difference equations Vol. 2020; no. 1; pp. 1 - 11
Main Authors: Khan, Shahid, Adil Khan, Muhammad, Butt, Saad Ihsan, Chu, Yu-Ming
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 06.07.2020
Springer Nature B.V
SpringerOpen
Subjects:
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
Online Access:Get full text
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-020-02794-8