Jensen and Hermite-Hadamard type inclusions for harmonical $ h $-Godunova-Levin functions-Reference-Cited by-同舟云学术

Jensen and Hermite-Hadamard type inclusions for harmonical $ h $-Godunova-Levin functions

Published:2023 Issue:2 Volume:8 Page:3303-3321
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Afzal Waqar¹²,Shabbir Khurram¹,Treanţă Savin³⁴⁵,Nonlaopon Kamsing⁶

Affiliation:

1. Department of Mathemtics, Government College University Lahore (GCUL), Lahore 54000, Pakistan

2. Department of Mathematics, University of Gujrat, Gujrat 50700, Pakistan

3. Department of Applied Mathematics, University Politehnica of Bucharest, Bucharest 060042, Romania

4. Academy of Romanian Scientists, 54 Splaiul Independentei, Bucharest 050094, Romania

5. Fundamental Sciences Applied in Engineering Research Center (SFAI), University Politehnica of Bucharest, Bucharest 060042, Romania

6. Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Abstract

<abstract><p>The role of integral inequalities can be seen in both applied and theoretical mathematics fields. According to the definition of convexity, it is possible to relate both concepts of convexity and integral inequality. Furthermore, convexity plays a key role in the topic of inclusions as a result of its definitional behavior. The importance and superior applications of convex functions are well known, particularly in the areas of integration, variational inequality, and optimization. In this paper, various types of inequalities are introduced using inclusion relations. The inclusion relation enables us firstly to derive some Hermite-Hadamard inequalities (H.H-inequalities) and then to present Jensen inequality for harmonical $ h $-Godunova-Levin interval-valued functions (GL-IVFS) via Riemann integral operator. Moreover, the findings presented in this study have been verified with the use of useful examples that are not trivial.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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