New quantum integral inequalities for left and right log-ℏ-convex interval-valued functions-Reference-Cited by-同舟云学术

New quantum integral inequalities for left and right log-ℏ-convex interval-valued functions

Published:2023-11-20 Issue:0 Volume:0 Page:
ISSN:1072-947X
Container-title:Georgian Mathematical Journal
language:en
Short-container-title:

Author:

Cheng Haiyang¹,Zhao Dafang²,Zhao Guohui³,Torres Delfim F. M.⁴

Affiliation:

1. School of Mathematics and Statistics , Hubei Normal University , Huangshi , 435002 , P. R. China

2. School of Mathematics and Statistics , Hubei Normal University , Huangshi , 435002 ; and National Cryosphere Desert Data Center, Lanzhou 730000 , P. R. China

3. National Cryosphere Desert Data Center , Lanzhou 730000; and Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences , Lanzhou 730000 , P. R. China

4. Center for Research and Development in Mathematics and Applications (CIDMA) , Department of Mathematics , University of Aveiro , 3810-193 Aveiro , Portugal

Abstract

Abstract We introduce the concept of quantum integration for interval-valued functions and establish new q-Hermite–Hadamard and q-Hermite–Hadamard–Fejér inequalities for left and right log ⁢ - ⁢ h

{\mathrm{log}\text{-}h}

-convex interval-valued functions. Our results generalize the known ones in the literature and serve as a foundation for future studies in inequalities for interval-valued functions and interval differential equations. We illustrate our results with examples.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/gmj-2023-2088/pdf

Reference43 articles.

1. M. Adil Khan, N. Mohammad, E. R. Nwaeze and Y.-M. Chu, Quantum Hermite-Hadamard inequality by means of a Green function, Adv. Difference Equ. 2020 (2020), Paper No. 99.

2. B. Ahmad, S. Ntouyas and J. Tariboon, Quantum Calculus. New Concepts, Impulsive IVPs and BVPs, Inequalities, Trends Abstr. Appl. Anal. 4, World Scientific, Hackensack, 2016.

3. M. A. Ali, H. Budak and Z. Zhang, A new extension of quantum Simpson’s and quantum Newton’s type inequalities for quantum differentiable convex functions, Math. Methods Appl. Sci. 45 (2022), no. 4, 1845–1863.

4. M. A. Ali, H. Budak, Z. Zhang and H. Yildirim, Some new Simpson’s type inequalities for coordinated convex functions in quantum calculus, Math. Methods Appl. Sci. 44 (2021), no. 6, 4515–4540.

5. N. Alp, M. Z. Sarıkaya, M. Kunt and İ. İşcan, q-Hermite–Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions, J. King Saud Univ. Sci. 30 (2018), no. 2, 193–203.