Results Math (2018) 73:88
2018 Springer International Publishing AG,
part of Springer Nature
Results in Mathematics
AdelaVall´ee Poussin Type Inequality
on Time Scales
Abstract. In this work we derive an inequality of the de la Vall´ee Poussin
type on a general time scale. In particular, we believe that a discrete
version of such inequality is presented for the ﬁrst time in the literature.
Mathematics Subject Classiﬁcation. Primary 26D10, Secondary 34N05.
Keywords. De la Vall´ee Poussin inequality, Lyapunov inequality, time
When we consider a second order boundary value problem, the following result
is known as the de la Vall´ee Poussin inequality (see e.g. ):
Theorem 1.1. Suppose that x ∈ C
[a, b], x =0on (a, b), is a solution of the
+ f(t)x =0,t∈ (a, b) (1.1)
where f,g ∈ C[a, b]. Then, the following inequality holds:
(b − a)+M
(b − a)
|g(t)| and M
Hartman and Wintner  generalized Theorem 1.1 in the following way:
Rui Ferreira was supported by the “Funda¸c˜aoparaaCiˆencia e a Tecnologia (FCT)” through
the program “Investigador FCT” with reference IF/01345/2014.