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JOURNALS // Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy // Archive

Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2025 Volume 12, Issue 1, Pages 129–143 (Mi vspua345)

MATHEMATICS

New Hermite-Hadamard fractional integral inequalities for $s$-geometry convex functions

H. Talebi, A. Neamaty

University of Mazandaran, Babolsar, Iran

Abstract: In the present study, we discuss some types of the Hermite-Hadamard (H-H) fractional integral inequality, with Riemann-Liouville fractional integral for functions whose absolute values of the first derivatives to positive real powers (AVFDPRP) are s-geometrically convex. That was concluded for geometrically convex as well. As an application, by using special mean of real numbers, H-H inequalities with ordinary integral were generalized for functions whose (AVFDPRP) are geometrically convex or s-geometrically convex.

Keywords: fractional integral, Hermite-Hadamard inequality, s-geometrically convex function.

UDC: 517.518.2

MSC: 26D15, 26A33, 26A51, 26E60

Received: 24.10.2023
Revised: 02.06.2024
Accepted: 29.08.2024

DOI: 10.21638/spbu01.2025.110



© Steklov Math. Inst. of RAS, 2025