Hermite-Hadamard Type Inequalities for Multiplicative Fractional Integrals of Log-Harmonically h -Convex Functions

This paper develops and extends Hermite-Hadamard type inequalities for log-harmonically [Formula: see text]-convex functions using multiplicative Riemann-Liouville fractional integrals within the context of multiplicative calculus. In particular, we establish new inequalities for the products and quotients of log-harmonically [Formula: see text]-convex functions. Furthermore, new inequalities involving multiplicative Riemann-Liouville fractional integrals are developed for combinations of log-harmonically [Formula: see text]-convex and harmonically convex functions, including their products and quotients. Numerical examples and graphical illustrations confirm the validity and practical relevance of the results.