Generalized fractional Hermite-Hadamard type inclusions for co-ordinated convex interval-valued functions

Miguel J. Vivas-Cortez; Hasan Kara; Hüseyin Budak; Muhammad Aamir Ali; Saowaluck Chasreechai

doi:10.1515/math-2022-0477

Generalized fractional Hermite-Hadamard type inclusions for co-ordinated convex interval-valued functions

Miguel J. Vivas-Cortez
, Hasan Kara
, Hüseyin Budak
, Muhammad Aamir Ali^*
, Saowaluck Chasreechai^*

^*Corresponding author for this work

Faculty of Exact and Natural Sciences

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

In this article, we introduce the notions of generalized fractional integrals for the interval-valued functions (IVFs) of two variables. We establish Hermite-Hadamard (H-H) type inequalities and some related inequalities for co-ordinated convex IVFs by using the newly defined integrals. The fundamental benefit of these inequalities is that these can be turned into classical H-H inequalities and Riemann-Liouville fractional H-H inequalities, and new k k -Riemann-Liouville fractional H-H inequalities can be obtained for co-ordinated convex IVFs without having to prove each one separately.

Original language	English
Pages (from-to)	1887-1903
Number of pages	17
Journal	Central European Journal of Mathematics
Volume	20
Issue number	1
DOIs	https://doi.org/10.1515/math-2022-0477
State	Published - 1 Jan 2022

Bibliographical note

Publisher Copyright:
© 2022 the author(s), published by De Gruyter.

Funding

Funding information : This work was also supported by King Mongkut’s University of Technology North Bangkok, Contract no. KMUTNB-63-KNOW-018.

Funders	Funder number
King Mongkut's University of Technology North Bangkok	KMUTNB-63-KNOW-018

Keywords

H-H inclusion
IVFs
co-ordinated convex
fractional integral
integral inclusions

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abstract = "In this article, we introduce the notions of generalized fractional integrals for the interval-valued functions (IVFs) of two variables. We establish Hermite-Hadamard (H-H) type inequalities and some related inequalities for co-ordinated convex IVFs by using the newly defined integrals. The fundamental benefit of these inequalities is that these can be turned into classical H-H inequalities and Riemann-Liouville fractional H-H inequalities, and new k k -Riemann-Liouville fractional H-H inequalities can be obtained for co-ordinated convex IVFs without having to prove each one separately.",

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AU - Kara, Hasan

AU - Budak, Hüseyin

AU - Ali, Muhammad Aamir

AU - Chasreechai, Saowaluck

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N2 - In this article, we introduce the notions of generalized fractional integrals for the interval-valued functions (IVFs) of two variables. We establish Hermite-Hadamard (H-H) type inequalities and some related inequalities for co-ordinated convex IVFs by using the newly defined integrals. The fundamental benefit of these inequalities is that these can be turned into classical H-H inequalities and Riemann-Liouville fractional H-H inequalities, and new k k -Riemann-Liouville fractional H-H inequalities can be obtained for co-ordinated convex IVFs without having to prove each one separately.

AB - In this article, we introduce the notions of generalized fractional integrals for the interval-valued functions (IVFs) of two variables. We establish Hermite-Hadamard (H-H) type inequalities and some related inequalities for co-ordinated convex IVFs by using the newly defined integrals. The fundamental benefit of these inequalities is that these can be turned into classical H-H inequalities and Riemann-Liouville fractional H-H inequalities, and new k k -Riemann-Liouville fractional H-H inequalities can be obtained for co-ordinated convex IVFs without having to prove each one separately.

KW - H-H inclusion

KW - IVFs

KW - co-ordinated convex

KW - fractional integral

KW - integral inclusions

UR - https://www.scopus.com/pages/publications/85146529981

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DO - 10.1515/math-2022-0477

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JF - Central European Journal of Mathematics

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ER -

Generalized fractional Hermite-Hadamard type inclusions for co-ordinated convex interval-valued functions

Abstract

Bibliographical note

Funding

Keywords

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