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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Veröffentlicht in:Demonstratio mathematica Jg. 55; H. 1; S. 387 - 403
Hauptverfasser: Khan, Muhammad Bilal, Noor, Muhammad Aslam, Macías-Díaz, Jorge E., Soliman, Mohamed S., Zaini, Hatim Ghazi
Format: Journal Article
Sprache:Englisch
Veröffentlicht: De Gruyter 13.08.2022
Schlagworte:
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
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Zusammenfassung: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