FURTHER ON OPIAL TYPE INTEGRAL INEQUALITIES FOR SUPERQUADRATIC FUNCTIONS

Xiujun Zhang, Ghulam Farid, Ayesha Bibi, Kamsing Nonlaopon and Tao Yan
Additional contact information
Xiujun Zhang: School of Computer Science, Chengdu University, Chengdu 610106, P. R. China
Ghulam Farid: ��Department of Mathematics, COMSATS University Islamabad, Attock 43600, Pakistan
Ayesha Bibi: ��Government Girls High School Behboodi, Hazro 43440, Pakistan
Kamsing Nonlaopon: �Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
Tao Yan: School of Computer Science, Chengdu University, Chengdu 610106, P. R. China

FRACTALS (fractals), 2023, vol. 31, issue 04, 1-12

Abstract: The following inequality ∫0c|ψ(z)ψ′(z)|dz ≤ c 4∫0c(ψ′(z))2dz is well known in the literature as Opial’s inequality [Z. Opial, Sur une inégalité, Polon. Math. 8 (1960) 29–32], it had/has been studied extensively since its appearance. This paper investigates some of its generalizations in the prospect of generalized integral operators. From huge literature on this inequality, the results for superquadratic functions are considered and further analyzed for some integral operators. Several inequalities have been deduced for fractional integral operators by analyzing particular kernels.

Keywords: Convex Function; Superquadratic Function; Opial’s Inequality; Fractional Integral Operators (search for similar items in EconPapers)
Date: 2023
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0218348X23400571
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:31:y:2023:i:04:n:s0218348x23400571

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0218348X23400571

Access Statistics for this article

FRACTALS (fractals) is currently edited by Tara Taylor

More articles in FRACTALS (fractals) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().