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Hardy-Type Tauberian Conditions on Time Scales

  • Ceylan Turan Yalçın
  • Oktay Duman
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Abstract

Hardy’s well-known Tauberian theorem for number sequences states that if a sequence \(x=\left( x_{k}\right) \) satisfies \(\lim Cx=L\) and \(\Delta x_{k}:=x_{k+1}-x_{k}=O\left( 1/k\right) \), 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.

Keywords

Tauberian theorems Cesàro summability Statistical convergence Time scales 

Mathematics Subject Classification

40E05 40G15 26E70 
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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsTOBB Economics and Technology UniversityAnkaraTurkey

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