Improvements of Slater's Inequality by Means of 4-Convexity and Its Applications

Xuexiao You, Muhammad Adil Khan, Hidayat Ullah, Tareq Saeed
2022 Mathematics  
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
more » ... , Shannon entropy, and Bhattacharyya coefficient. In addition, we discuss some additional applications of the main results for the Zipf–Mandelbrot entropy.
doi:10.3390/math10081274 fatcat:nhz6vqgznjck3g6mtqahjlwqmq