Abstract
The Jensen inequality has been reported as one of the most consequential inequalities that has a lot of applications in diverse fields of science. For this reason, the Jensen inequality has become one of the most discussed developmental inequalities in the current literature on mathematical inequalities. The main intention of this article is to find some novel bounds for the Jensen difference while using some classes of twice differentiable convex functions. We obtain the proposed bounds by utilizing the power mean and Höilder inequalities, the notion of convexity and the prominent Jensen inequality for concave function. We deduce several inequalities for power and quasi-arithmetic means as a consequence of main results. Furthermore, we also establish different improvements for Hölder inequality with the help of obtained results. Moreover, we present some applications of the main results in information theory.
Highlights
Academic Editor: Milica Klaricic BakulaReceived: 22 November 2021Accepted: 1 December 2021Published: 5 December 2021Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil-The notion of convexity has played a very fundamental role in the last century with a dynamic impact on the several areas of science including Engineering [1], Statistics [2], Economics [3], Optimization [4] and Information Theory [5], etc
For the obtaining of proposed bounds, we shall use the notion of convexity, Jensen’s inequality for concave functions, Hölder and power mean inequalities
We commence this section with the following theorem, in which a bound for the Jensen difference is obtained with the help of Hölder inequality and definition of convex function
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil-. Nakasuji and Takahasi [14] used a convex function from topological abelian semi group to topological ordered abelian semigroup and obtained a finite form of Jensen’s inequality They gave an application of their main result in the form a refinement of mean inequality. Khan et al [17] proposed a new method of finding estimates for the Jensen differences by choosing differentiable functions and discussed some improvements of Hermite–Hadamard and Hölder inequalities They deliberated inequalities for different means and granted applications of their main results in information theory. In 2021, Deng et al [5] proved some refinements of Jensen’s inequality with the help of majorization results while using the notion of convexity They provided some refinements for classical inequalities and presented applications of main results. Jensen’s inequality, see [19,20,21]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
