Some inequalities of Hermite-Hadamard type for n--times differentiable (ρ,m )--geometrically convex functions

In this paper, some generalized Hermite-Hadamard type inequalities for n-times differentiable (\(ρ, m\))- geometrically convex function are established. The new inequalities recapture and give new estimates of the previous inequalities for first differentiable functions as special cases. The estimates for trapezoid, midpoint, averaged mid-point trapezoid and Simpson's inequalities can also be obtained for higher differentiable generalized geometrically convex functions.