Several new cyclic Jensen type inequalities and their applications

We present some fundamental results and definitions regarding Jensen’s inequality with the aim of obtaining new generalizations of cyclic refinements of Jensen’s inequality from convex to higher order convex functions using Taylor’s formula. We discuss the monotonicity of functionals for n-convex functions at a point. Applications of our work include new bounds for some important inequalities used in information theory. © 2019, The Author(s).

Authors
Mehmood N.1 , Butt S.I.1 , Pečarić Ð.2 , Pečarić J. 3
Journal
Journal of Inequalities and Applications
Publisher
Springer International Publishing
Number of issue
1
Language
English
Status
Published
Link
External link
DOI
10.1186/s13660-019-2191-7
Number
240
Volume
2019
Year
2019
Organizations
  • 1 Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan
  • 2 Catholic University of Croatia, Zagreb, Croatia
  • 3 RUDN University, Moscow, Russian Federation
Keywords
Higher order convexity; Jensen’s inequality; Kullback–Leibler divergence; New Green functions; Shannon entropy; Taylor’s formula; Zipf–Mandelbrot entropy
Date of creation
24.12.2019
Date of change
24.12.2019
Short link
https://repository.rudn.ru/en/records/article/record/55427/
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