In this paper, we introduce a new class of convex function, which is called coordinated exponentially m-convex functions. Some new Petrovic’s type inequalities for exponentially m-convex functions and coordinated exponentially m-convex functions are derived. Lagrange-type and Cauchy-type mean value theorems for exponentially m−convex and coordinated exponentially m-convex functions are also derived. Several special cases are discussed. We also prove the Lagrange type and Cauchy type mean value theorems for exponentially m-convex and coordinated exponentially m−convex functions. Results proved in this paper may stimulate further research in different areas of pure and applied sciences.