Statistically pre-Cauchy sequences and bounded moduli

  • Mehmet Gürdal Suleyman Demirel University
Keywords: statistically convergent sequence, statistically pre-Cauchy sequence, modulus function

Abstract

Let x=(xk) be a sequence and let f be a bounded modulus. We prove that x is statistically pre-Cauchy if and only if 

limn 1/n2j,k≤nf(|xk−xj|)=0.

This implies a theorem due to Connor, Fridy and Kline [4].

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Author Biography

Mehmet Gürdal, Suleyman Demirel University

Department of Mathematics

Published
2003-12-31
Section
Articles