Abstract
In this study, we extend some “sneak-out” inequalities on time scales for a function depending on more than one parameter. The results are proved by using the induction principle and time scale version of Minkowski inequalities. In seeking applications, these inequalities are discussed in classical, discrete, and quantum calculus.
Highlights
If a function g: T ⟶ R is continuous at all right-dense points, the left-hand limits exist and are finite at left-dense points in T; it is right-dense continuous on T. e set denoted by Cr d(T) contain all rdcontinuous functions on T
We prove the result by using mathematical induction
By mathematical induction, (14) is true for all h ∈ N
Summary
e paper is organized as follows. Section 2 provides some basics from time scales’ calculus. Section 3 features two dynamic inequalities of the Copson type, which are needed to prove further results. In Section 4, we present sneak-out inequalities on time scales for functions depending on more than one parameter.
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