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...-Levin functions and P -functions, which are obtained by putting in (1.2), h(t) = t, h(t) = ts, h(t) = 1 t , and h(t) = 1, respectively. Many properties of them can be found, for instance, in [6],[7],=-=[16]-=-,[18],[19],[21],[23]. Let us consider a function ϕ : [a, b] → [a, b] where [a, b] ⊂ R. Youness have defined the ϕ-convex functions in [17]: Definition 1. A function f : [a, b]→ R is said to be ϕ- conv...

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...een introduced by Polyak in [13] and they play an important role in optimization theory and mathematical economics. Various properties and applicatins of them can be found in the literature see ([13]-=-=[16]-=-) and the references cited therein. In this paper we introduce the notation of strongly logarithmic convex with respect to c > 0 and versions of Hermite-Hadamard-type inequalities for strongly logarit...