The convex function is an important concept in the class mathematical analysis course.And many important inequalities are established for the class of convex functions.However,Hermite-Hadamards inequality is the one of the best know results in the literature.Hadamards inequality for convex functions has received renewed attention in recent years and a remarkable variety of refinements and generalizations have been found.In recent years,the fractal space and local fractional calculus have received significantly remarkable attention.In the sense of Mandelbrot,a fractal set is the one whose Hausdorff dimension strictly exceeds the topological dimension.The calculus on fractal set can lead to better comprehension for the various real world models from science and engineering.Analogous to the class situation,in the lecture we introduce the definition of the generalized convex function on fractal sets and study the properties of the generalized convex functions.Moreover,we established the generalized Jensens inequality and generalized Hermite-Hadamards inequality on fractal sets.And,by two identities about the local fractional integrals,we obtain some generalized Hermite-Hadamard type integral inequalities for the local differentiable generalized convex functions on fractal space.