On Some New Dynamic Inequalities Involving C-Monotonic Functions on Time Scales

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.