Further improvements of the Jensen inequality in the integral sense by virtue of 6-convexity along with applications-Reference-Cited by-同舟云学术

Further improvements of the Jensen inequality in the integral sense by virtue of 6-convexity along with applications

Published:2024 Issue:5 Volume:9 Page:11278-11303
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Sohail Asadullah¹,Khan Muhammad Adil¹,Nasr Emad Abouel²,Ding Xiaoye³

Affiliation:

1. Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan

2. Industrial Engineering Department, College of Engineering, King Saud University, Riyadh 11421, Saudi Arabia

3. General Education Department, Anhui Xinhua University, Hefei 230088, China

Abstract

<abstract><p>The Jensen inequality is of fundamental importance because of its influential and interesting consequences. In recent years, the Jensen inequality has been supposed to be the most engaging source for research. We present interesting improvements to the continuous version of Jensen's inequality through the application of the concept of 6-convexity. For real visualization and comparison to other results, some numerical experiments were provided. With the aid of the acquired results, improvements for the Hermite-Hadamard and Hölder inequalities were presented. Some relationships between the means were granted as applications of established improvements. In addition, some estimations of the Csiszár divergence and its associated cases were received as further applications of the obtained results. The major techniques employed in formulating the proposed improvements included the Jensen inequality and the concept of convexity.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Reference46 articles.

1. N. Mukhopadhyay, On sharp Jensen's inequality and some unusual applications, communications in statistics, Theor. Methods, 40 (2011), 1283–1297. https://doi.org/10.1080/03610920903580988

2. V. Lakshmikantham, A. S. Vatsala, Theory of differential and integral inequalities with initial time difference and applications, In: T. M. Rassias, H. M. Srivastava, Analytic and geometric inequalities and applications, Springer, 1999,191–203. https://doi.org/10.1007/978-94-011-4577-0_12

3. S. M. Ross, Introduction to probability models, Academic Press, 2014.

4. A. W. van der Vaart, Asymptotic statistics, Cambridge University Press, 2000. https://doi.org/10.1017/CBO9780511802256

5. H. H. Chu, H. Kalsoom, S. Rashid, M. Idrees, F. Safdar, Y. M. Chu, et al., Quantum analogs of Ostrowski-type inequalities for Raina's function correlated with coordinated generalized $\Phi$-convex functions, Symmetry, 12 (2020), 308. https://doi.org/10.3390/sym12020308