New Jensen's bounds for HA-convex mappings with applications to Shannon entropy

Yamin Sayyari; Saad Ihsan Butt; Mehdi Dehghanian; Praveen Agarwal; Juan J. Nieto

doi:10.1515/dema-2025-0122

New Jensen's bounds for HA-convex mappings with applications to Shannon entropy

Yamin Sayyari
, Saad Ihsan Butt
, Mehdi Dehghanian
, Praveen Agarwal
, Juan J. Nieto

Nonlinear Dynamic Research Centre (NDRC)

Sirjan University of Technology
COMSATS University Islamabad
Saveetha Institute of Medical and Technical Sciences (Deemed to be University)
International College of Engineering
Universidade de Santiago de Compostela

Research output: Contribution to journal › Article › peer-review

Abstract

The aim of this article is to establish some new extensions and variants of Jensen's discrete and Simic-type inequalities for HA-convex and uniformly HA-convex functions. We introduce uniformly HA-convex functions, which are the generalized class of HA-convex (harmonic-arithmetic)-convex functions and provide some examples too. As an application point of view for the new Jensen's bounds, we present some new improved bounds for Shannon's entropy. Finally, some analysis is given by graphical illustration to prove the improvements of bounds.

Original language	English
Article number	20250122
Journal	Demonstratio Mathematica
Volume	58
Issue number	1
DOIs	https://doi.org/10.1515/dema-2025-0122
State	Published - 1 Jan 2025

Keywords

HA-convex function
Jensen's inequality
Shannon's entropy
uniformly HA-convex function

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10.1515/dema-2025-0122

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abstract = "The aim of this article is to establish some new extensions and variants of Jensen's discrete and Simic-type inequalities for HA-convex and uniformly HA-convex functions. We introduce uniformly HA-convex functions, which are the generalized class of HA-convex (harmonic-arithmetic)-convex functions and provide some examples too. As an application point of view for the new Jensen's bounds, we present some new improved bounds for Shannon's entropy. Finally, some analysis is given by graphical illustration to prove the improvements of bounds.",

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AU - Nieto, Juan J.

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N2 - The aim of this article is to establish some new extensions and variants of Jensen's discrete and Simic-type inequalities for HA-convex and uniformly HA-convex functions. We introduce uniformly HA-convex functions, which are the generalized class of HA-convex (harmonic-arithmetic)-convex functions and provide some examples too. As an application point of view for the new Jensen's bounds, we present some new improved bounds for Shannon's entropy. Finally, some analysis is given by graphical illustration to prove the improvements of bounds.

AB - The aim of this article is to establish some new extensions and variants of Jensen's discrete and Simic-type inequalities for HA-convex and uniformly HA-convex functions. We introduce uniformly HA-convex functions, which are the generalized class of HA-convex (harmonic-arithmetic)-convex functions and provide some examples too. As an application point of view for the new Jensen's bounds, we present some new improved bounds for Shannon's entropy. Finally, some analysis is given by graphical illustration to prove the improvements of bounds.

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KW - Shannon's entropy

KW - uniformly HA-convex function

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New Jensen's bounds for HA-convex mappings with applications to Shannon entropy

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Keywords

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