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

Khan Muhammad Bilal, Noor Muhammad Aslam, Macías-Díaz Jorge E., Soliman Mohamed S., Zaini Hatim Ghazi

Demonstratio Mathematica

2022

Vol. 55, nr 1

387--403

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- s -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- s -convex-IVFs. Therefore, we establish some new Jensen-type, Hermite-Hadamard (HH)-type, and Hermite-Hadamard-Fejér (HH-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- s -convex IVFs.

The Jensen inequality for s-Breckner convex functions in linear spaces

Dragomir S. S., Fitzpatrick S.

Demonstratio Mathematica

2000

Vol. 33, nr 1

43-49

We derive some inequalities of Jensen's type for 5-convex functions in the sense of Breckner on subsets of linear spaces and give some applications connected with special means.