Estimations of the Jensen Gap and Their Applications Based on 6-Convexity

Autor:	Muhammad Adil Khan, Asadullah Sohail, Hidayat Ullah, Tareq Saeed
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	convex function 6-convex function Jensen’s inequality Hölder inequality power means quasi-arithmetic means Mathematics QA1-939
Zdroj:	Mathematics, Vol 11, Iss 8, p 1957 (2023)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math11081957
Popis:	The main purpose of this manuscript is to present some new estimations of the Jensen gap in a discrete sense along with their applications. The proposed estimations for the Jensen gap are provided with the help of the notion of 6-convex functions. Some numerical experiments are performed to determine the significance and correctness of the intended estimates. Several outcomes of the main results are discussed for the Hölder inequality and the power and quasi-arithmetic means. Furthermore, some applications are presented in information theory, which provide some bounds for the divergences, Bhattacharyya coefficient, Shannon entropy, and Zipf–Mandelbrot entropy.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/7ab4f341be64400d9edbe6c1056212a1 Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF Plný text ve formátu HTML
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