Some integral inequalities for generalized left and right log convex interval-valued functions based upon the pseudo-order relation

It is a well-known fact that inclusion and pseudo-order relations are two different concepts which are defined on the interval spaces, and we can define different types of convexities with the help of both relations. By means of pseudo-order relation, the present article deals with the new notions o...

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Bibliographic Details
Published in:	Demonstratio mathematica Vol. 55; no. 1; pp. 387 - 403
Main Authors:	Khan, Muhammad Bilal, Noor, Muhammad Aslam, Macías-Díaz, Jorge E., Soliman, Mohamed S., Zaini, Hatim Ghazi
Format:	Journal Article
Language:	English
Published:	De Gruyter 13.08.2022
Subjects:	26A33 26A51 26D10 convex interval-valued functions Hermite-Hadamard-Fejér-type inequality Hermite-Hadamard-type inequality Jensen’s inequality left and right log left and right log-s-convex interval-valued functions
ISSN:	2391-4661, 2391-4661
Online Access:	Get full text
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Summary:	It is a well-known fact that inclusion and pseudo-order relations are two different concepts which are defined on the interval spaces, and we can define different types of convexities with the help of both relations. By means of pseudo-order relation, the present article deals with the new notions of convex functions which are known as left and right log- -convex interval-valued functions (IVFs) in the second sense. The main motivation of this study is to present new inequalities for left and right log- -convex-IVFs. Therefore, we establish some new Jensen-type, Hermite-Hadamard ( )-type, and Hermite-Hadamard-Fejér ( -Fejér)-type inequalities for this kind of IVF, which generalize some known results. To strengthen our main results, we provide nontrivial examples of left and right log- -convex IVFs.
ISSN:	2391-4661 2391-4661
DOI:	10.1515/dema-2022-0023