Hardy-Type Tauberian Conditions on Time Scales

Abstract

Hardy’s well-known Tauberian theorem for number sequences states that if a sequence x= (xk) satisfies lim Cx= L and Δ xk: = xk + 1- xk= O(1 / k) , then lim x= L, where Cx denotes the Cesàro mean (arithmetic mean) of x. In this study, we extend this result to the theory of time scales. We also discuss the theory on some special time scales.