SOME REMARKS ON FUNCTIONS WITH NON-DECREASING INCREMENTS

The main purpose of this work is to establish relationship of functions with non-decreasing increments with other functions of high importance. Especially, we pay attention to the role of representation and connection among functions with non-decreasing increments and arithmetic integral mean, Wright convex functions, convex functions, del-convex functions, Jensen m-connvex functions, m-convex functions, m - del -convex functions, k-monotonic functions, absolutely monotonic functions, completely monotonic functions, Laplace Transform and exponentially convex functions, by using the method of finite difference operator as different cases of Delta(m)(h) f (y). We also consider function with non-decreasing increments of order three and obtain the generalisation of the Levinson's-type inequality and Jensen-Mercer's-type inequality by using Jensen-Boas inequality and also deduce some results.