Generalized Ostrowski’s Inequality on Time Scales

The Discrete Version of Ostrowski’s Inequality in Normed Linear Spaces

Discrete versions of Ostrowski’s inequality for vectors in normed linear spaces are given.

Some new variants of interval-valued Gronwall type inequalities on time scales

By using an efficient partial order and concept of gH-differentiability oninterval-valued functions, we investigate some new variants of Gronwall typeinequalities on time scales, which provide explicit bounds on unknownfunctions. Our results not only unify and extend some continuousinequalities, but also in discrete case, all are new.

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. S...

A Companion of Ostrowski’s Inequality for the Riemann-stieltjes Integral

A Generalized Gronwall–bellman Type Delay Integral Inequality with Two Independent Variables on Time Scales

Using a technique of monotonization, this paper investigates a generalized GronwallBellman type delay integral inequality with two independent variables on time scales. The result not only unifies some continuous inequalities and their discrete analogues but also extends some known integral inequalities on time scales. An application to the estimation of solutions of delay dynamic integral equa...