ANALYSIS ON MULTIPLICATIVELY (P,m)-SUPERQUADRATIC FUNCTIONS AND RELATED FRACTIONAL INEQUALITIES WITH APPLICATIONS

Dawood Khan (), Saad Ihsan Butt () and Youngsoo Seol
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Dawood Khan: Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan
Saad Ihsan Butt: Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan
Youngsoo Seol: ��Department of Mathematics, Dong-A University, Busan 49315, Korea

FRACTALS (fractals), 2025, vol. 33, issue 03, 1-27

Abstract: In this work, we, for the first time, establish a class of multiplicatively (P,m)-superquadratic function and look into its various features. In the light of these features, we come up with the several integer order integral inequalities in the frame of multiplicative calculus. Moreover, we develop the fractional version of Hermite–Hadamard’s type inequalities involving midpoints and end points for multiplicatively (P,m)-superquadratic function with respect to multiplicatively k-Riemann–Liouville fractional integrals. By choosing different values for the parameters of such integral operators, we acquire a simple version of integral inequalities of Hermite–Hadamard’s type as well as its fractional form via multiplicatively Riemann–Liouville fractional integrals for multiplicatively (P,m)-superquadratic function. The findings are confirmed by graphical illustration by taking appropriate examples into account. The study is further enhanced by the addition of applications of special means and first-type modified Bessel functions. The new results clearly provide extensions and improvements of the work available in the literature.

Keywords: Superquadratic Function; Multiplicatively (P; m)-Superquadratic Function; Multiplicative Calculus; Hermite–Hadamard’s Inequality; Multiplicatively k-Riemann–Liouville Fractional Integral; First-Type Modified Bessel Function (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X24501299

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