LAUSR

In this paper, we establish some new dynamic inequalities involving C-monotonic functions with C≥1, on time scales. As a special case of our results when C=1, we obtain the inequalities involving increasing or decreasing functions (where for C=1, the 1-decreasing function is decreasing and the 1-increasing function is increasing). The main results are proved by applying the properties of C-monotonic functions and the chain rule formula on time scales. As a special case of our results, when T=R, we obtain refinements of some well-known continuous inequalities and when T=N, to the best of the authors’ knowledge, the results are essentially new.