A New Generalization of Ostrowski Type Inequality on Time Scales

(b− a)‖f ‖∞. (1) The inequality is sharp in the sense that the constant 14 cannot be replaced by a smaller one. For some extensions, generalizations and similar results, see [6, 9, 10, 11, 13, 14] and references therein. The development of the theory of time scales was initiated by Hilger [7] in 1988 as a theory capable to contain both difference and differential calculus in a consistent way. Since then, many authors have studied the theory of certain integral inequalities on time scales. For example, we refer the reader to [1, 4, 5, 15, 16]. In [5], Bohner and Matthews established the following so-called Ostrowski’s inequality on time scales. Theorem 1.2 (See [5], Theorem 3.5). Let a, b, s, t ∈ T, a < b and f : [a, b] → R be differentiable. Then