m-Convex Functions on Time Scale

Abstract

Convex functions play a key role in different field of mathematics such as in the theory of inequalities. m-convex function is the generalization of convex function. The calculus and applications of dynamic derivatives defined on time scales give unification as well as an extension of customary differential and difference equations. This dissertation deals with the notion of m-convex function on time scale. Some basic and well-known inequalities have been deduced such as Petrovic’s, Jensen’s, Hermite-Hadamard and Fejer’s. Also Hermite-Hadamard and Petrovic’s inequalities have been discussed in the two coordinated m-convex function on time scale.