Hermite-Hadamard type inequalities for logarithmically B-preinvex functions

In this paper, we introduce the notion of logarithmically B-preinvex functions and establish certain new Hermite-Hadamard type inequalities for the functions whose derivatives in absolute value are logarithmically B-preinvex. Our results generalize several known results for the classes of logarithmically preinvex functions. Some estimates for the left and right hand side of the Hermite-Hadamard inequality are also obtained for a new class of differentiable logarithmically α -preinvex functions.