Open AccessHermite-Hadamard like inequalities for fractional integral operator via convexity and quasi-convexity with their applications
Author(s) -
Jamshed Nasir,
Shahid Qaisar,
Saad Ihsan Butt,
Hassen Aydi,
M. De La Sen
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022190
Subject(s) - hermite polynomials , hadamard transform , mathematics , convex function , convexity , pure mathematics , bessel function , operator (biology) , jensen's inequality , type (biology) , mathematical analysis , regular polygon , convex optimization , convex analysis , geometry , ecology , biochemistry , chemistry , repressor , biology , transcription factor , financial economics , economics , gene
Since the supposed Hermite-Hadamard inequality for a convex function was discussed, its expansions, refinements, and variations, which are called Hermite-Hadamard type inequalities, have been widely explored. The main objective of this article is to acquire new Hermite-Hadamard type inequalities employing the Riemann-Liouville fractional operator for functions whose third derivatives of absolute values are convex and quasi-convex in nature. Some special cases of the newly presented results are discussed as well. As applications, several estimates concerning Bessel functions and special means of real numbers are illustrated.