Upper and lower estimations of Popoviciu’s difference via weighted Hadamard inequality with applications-Reference-Cited by-同舟云学术

Upper and lower estimations of Popoviciu’s difference via weighted Hadamard inequality with applications

Published:2023 Issue:22 Volume:37 Page:7641-7662
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Butt S.I.¹,Rasheed T.¹,Pecaric D.²,Pecaric J.³

Affiliation:

1. COMSATS University Islamabad, Lahore Campus Pakistan

2. Department of Media and Communication, University North, Koprivnica, Croatia

3. Croatian Academy of Sciences and Arts, Zagreb, Croatia

Abstract

We consider differences coming from Popoviciu?s inequality and give upper and lower bounds by employing weighted Hermite-Hadamard inequality along with the approximations of Montgomery two point formula. We also give bounds for Popoviciu?s inequality by employing weighted Hermite-Hadamard inequality along with the approximations of Montgomery one point formula. We testify this scenario by utilizing the theory of n-times differentiable convex functions. Our results hold for all n ? 2 and we provide explicit examples to show the correctness of the bounds obtained for special cases. Last but not least, we provide applications in information theory by providing new uniform estimations of the generalized Csiszar divergence, Renyi-divergence, Shannon-entropy, Kullback-Leibler divergence, Zipf and Hybrid Zipf-Mandelbrot entropies.

Publisher

National Library of Serbia

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