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  • Research Article
  • Open Access

Subsequential Convergence Conditions

Journal of Inequalities and Applications20072007:087414

https://doi.org/10.1155/2007/87414

  • Received: 27 April 2007
  • Accepted: 19 August 2007
  • Published:

Abstract

Let be a sequence of real numbers and let be any regular limitable method. We prove that, under some assumptions, if a sequence or its generator sequence generated regularly by a sequence in a class of sequences is a subsequential convergence condition for , then for any integer , the repeated arithmetic means of , , generated regularly by a sequence in the class , is also a subsequential convergence condition for .

Keywords

  • Generator Sequence
  • Real Number
  • Convergence Condition
  • Limitable Method
  • Arithmetic Means

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Authors’ Affiliations

(1)
Department of Mathematics, Adnan Menderes University, Aydin, 09010, Turkey
(2)
Department of Mathematics, Rockford College, 5050 E. State Street, Rockford, IL 61108, USA

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