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In this paper, some new integral inequalities of Hermite-Hadamard type are presented for functions whose nth derivatives in absolute value are s-logarithmically convex. From our results, several inequalities of Hermite-Hadamard type can be derived in terms of functions whose first and second derivatives in absolute value are s-logarithmically convex functions as special cases. Our results may provide refinements of some results for s-logarithmically convex functions already exist in literature. Finally, applications to special means of the established results are given. 2010 Mathematics Subject Classification: 26D15; 26D20; 26E60; 41A55

New integral inequalities of Hermite-Hadamard type for $n$-times differentiable $s$-logarithimcally convex functions with applications