Symmetrical Hermite-Hadamard type inequalities stemming from multiplicative fractional integrals

We firstly study *integrability and commutativity for multiplicative fractional integrals with exponential kernels, proposed by Peng et al. (2022). Secondly, making use of such operators, we present a symmetrical multiplicative fractional integrals identity. Based on it, and the fact that the function T* is multiplicatively convex or the function (ln T*)(theta) is convex for theta > 1, especially pondering the case of 0 < theta <= 1, we establish the symmetrical Hermite-Hadamard type inequalities for multiplicative convexity. We also give some applications in special means under multiplicative calculus.