Abstract
We develop a fresh family of functions, called as multiplicatively (P,m)-convex functions. In this direction, we study the properties of such type functions, and establish integer-order inequalities of Hermite–Hadamard type. After that, we introduce the multiplicative k-Riemann–Liouville fractional integrals and discuss their ⁎integrability, continuity as well as commutativity. Based on the proposed integral operators and the fact that the function is multiplicatively (P,m)-convex or (P,m)-convex, we derive some k-Riemann–Liouville fractional Hermite–Hadamard- and Newton-type inequalities. In the meantime, we provide certain examples together with their graphical descriptions, from which support the correctness of the inequalities obtained here. Some applications in special means are provided as well.
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