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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

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2022

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Vol. 55, nr 1

387--403

EN

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.

2

Some Hermite-Hadamard type integral inequalities for convex functions defined on convex bodies in Rn\mathbb{R}^{n}

Dragomir Silvestru Sever

Journal of Applied Analysis

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2020

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Vol. 26, nr 1

67--77

EN

In this paper, by the use of the divergence theorem, we establish some integral inequalities of Hermite-Hadamard type for convex functions of several variables defined on closed and bounded convex bodies in the Euclidean space Rn for any n ≥ 2.

3

Generalization of different type integral inequalities for generalized (s, m)-preinvex Godunova-Levin functions

Kashuri A., Liko R.

Journal of Applied Analysis

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2018

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Vol. 24, nr 2

211--221

EN

In the present paper, the notion of generalized (s, m)-preinvex Godunova-Levin function of second kind is introduced, and some new integral inequalities involving generalized (s, m)-preinvex Godunova-Levin functions of second kind along with beta function are given. By using a new identity for fractional integrals, some new estimates on generalizations of Hermite-Hadamard, Ostrowski and Simpson type inequalities for generalized (s, m)-preinvex Godunova-Levin functions of second kind via Riemann-Liouville fractional integral are established.

4

Generalized Ostrowski type inequalities for functions whose local fractional derivatives are generalized s-convex in the second sense

Budak H., Sarikaya M. Z., Set E.

Journal of Applied Mathematics and Computational Mechanics

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2016

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Vol. 15, nr 4

11-21

EN

In this paper, we establish some generalized Ostrowski type inequalities for functions whose local fractional derivatives are generalized s-convex in the second sense.

5

Hermite–Hadamard type inequalities for extended s-convex functions on the co-ordinates in a rectangle

Xi B.-Y, Hua J., Qi F.

Journal of Applied Analysis

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2014

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Vol. 20, nr 1

29--39

EN

In the paper, the authors obtain some Hermite–Hadamard type integral inequalities for extended s-convex functions on the co-ordinates in a rectangle.

6

Hermite-Hadamard inequalities for convex set-valued functions

Mitroi F. C., Nikodem K., Wąsowicz S.

Demonstratio Mathematica

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2013

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Vol. 46, nr 4

655--662

EN

The following version of the weighted Hermite-Hadamard inequalities for set-valued functions is presented: Let Y be a Banach space and F : [a, b]→cl(Y) be a continuous set-valued function. If F is convex, then (…) , where μ is a Borel measure on [a, b] and xμ is the barycenter of on [a, b]. The converse result is also given.

7

On some new inequalities of Hermite-Hadamard-Fejer type involving convex functions

Tseng K., Hwang S., Dragomir S.

Demonstratio Mathematica

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2007

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Vol. 40, nr 1

51-64

EN

In this paper, we establish some inequalities of Hermite-Hadamard-Fejér type for m-convex functions and s-convex functions.