Multiplicative Fractional Hermite–Hadamard-Type Inequalities in G -Calculus

Abdelghani Lakhdari and Wedad Saleh ()
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Abdelghani Lakhdari: Department of Mathematics, Faculty of Science and Arts, Kocaeli University, Umuttepe Campus, Kocaeli 41001, Türkiye
Wedad Saleh: Department of Mathematics, College of Science, Taibah University, Al-Medina 42210, Saudi Arabia

Mathematics, 2025, vol. 13, issue 21, 1-24

Abstract: This paper extends Hermite–Hadamard-type inequalities to the fractional multiplicative framework of G -calculus. Using multiplicative Riemann–Liouville fractional integrals, we introduce a notion of multiplicative convexity and establish fractional Hermite–Hadamard, midpoint, and trapezoidal inequalities for G G -convex functions. Examples and graphical illustrations are provided to demonstrate the applicability of our results and further highlight the role of fractional multiplicative analysis in broadening traditional integral inequalities.

Keywords: G -calculus; multiplicative Riemann–Liouville fractional integrals; GG -convex functions; GA -convex functions; Hermite–Hadamard inequality; multiplicative midpoint inequality; multiplicative trapezium inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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