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Search Results (4)

Search Parameters:
Keywords = discrete power mean inequality

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12 pages, 282 KiB  
Article
Some Simpson-like Inequalities Involving the (s,m)-Preinvexity
by Tarek Chiheb, Badreddine Meftah, Abdelkader Moumen, Mouataz Billah Mesmouli and Mohamed Bouye
Symmetry 2023, 15(12), 2178; https://doi.org/10.3390/sym15122178 - 8 Dec 2023
Cited by 1 | Viewed by 1072
Abstract
In this article, closed Newton–Cotes-type symmetrical inequalities involving four-point functions whose second derivatives are (s,m)-preinvex in the second sense are established. Some applications to quadrature formulas as well as inequalities involving special means are provided. Full article
(This article belongs to the Special Issue Symmetry in Functional Equations and Inequalities, 2nd Edition)
25 pages, 398 KiB  
Article
Estimations of the Jensen Gap and Their Applications Based on 6-Convexity
by Muhammad Adil Khan, Asadullah Sohail, Hidayat Ullah and Tareq Saeed
Mathematics 2023, 11(8), 1957; https://doi.org/10.3390/math11081957 - 20 Apr 2023
Cited by 7 | Viewed by 2172
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Mathematical Inequalities, Models and Applications)
19 pages, 336 KiB  
Article
Improvements of Slater’s Inequality by Means of 4-Convexity and Its Applications
by Xuexiao You, Muhammad Adil Khan, Hidayat Ullah and Tareq Saeed
Mathematics 2022, 10(8), 1274; https://doi.org/10.3390/math10081274 - 12 Apr 2022
Cited by 13 | Viewed by 1964
Abstract
In 2021, Ullah et al., introduced a new approach for the derivation of results for Jensen’s inequality. The purpose of this article, is to use the same technique and to derive improvements of Slater’s inequality. The planned improvements are demonstrated in both discrete [...] Read more.
In 2021, Ullah et al., introduced a new approach for the derivation of results for Jensen’s inequality. The purpose of this article, is to use the same technique and to derive improvements of Slater’s inequality. The planned improvements are demonstrated in both discrete as well as in integral versions. The quoted results allow us to provide relationships for the power means. Moreover, with the help of established results, we present some estimates for the Csiszár and Kullback–Leibler divergences, Shannon entropy, and Bhattacharyya coefficient. In addition, we discuss some additional applications of the main results for the Zipf–Mandelbrot entropy. Full article
(This article belongs to the Special Issue Recent Trends in Convex Analysis and Mathematical Inequalities)
18 pages, 319 KiB  
Article
Refinement of Discrete Lah–Ribarič Inequality and Applications on Csiszár Divergence
by Đilda Pečarić, Josip Pečarić and Jurica Perić
Mathematics 2022, 10(5), 755; https://doi.org/10.3390/math10050755 - 26 Feb 2022
Cited by 1 | Viewed by 1486
Abstract
In this paper we give a new refinement of the Lah–Ribarič inequality and, using the same technique, we give a refinement of the Jensen inequality. Using these results, a refinement of the discrete Hölder inequality and a refinement of some inequalities for discrete [...] Read more.
In this paper we give a new refinement of the Lah–Ribarič inequality and, using the same technique, we give a refinement of the Jensen inequality. Using these results, a refinement of the discrete Hölder inequality and a refinement of some inequalities for discrete weighted power means and discrete weighted quasi-arithmetic means are obtained. We also give applications in the information theory; namely, we give some interesting estimations for the discrete Csiszár divergence and for its important special cases. Full article
(This article belongs to the Special Issue Mathematical Inequalities with Applications)
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