Geometrically Relative Convex Functions

In this paper, some new concepts of geometrically relative convex sets and relative convex functions are defined. These new classes of geometrically relative convex functions unify several known and new classes of relative convex functions such as exponential convex functions. New Hermite-Hadamard type integral inequalities are derived for these new classes of geometrically relative convex functions and their variant forms. Some special cases, which can be obtained from our results, are discussed. Results proved in this paper represent significant improvements of the previously known results. We would like to emphasize that the results obtained and discussed in this paper may stimulate novel, innovative and potential applications of the geometrically relative convex functions in other fields.