Lacunary statistical and sliding window convergence for measurable functions

Connor J., Savaş E.

Acta Mathematica Hungarica, vol.145, no.2, pp.416-432, 2015 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 145 Issue: 2
  • Publication Date: 2015
  • Doi Number: 10.1007/s10474-015-0481-1
  • Journal Name: Acta Mathematica Hungarica
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.416-432
  • Keywords: Cauchy criteria, lacunary statistical convergence, measurable functions, sliding window method, statistical convergence
  • Uşak University Affiliated: No

Abstract

A class of summability methods, called sliding window methods, for measurable real valued functions defined on [0, ∞) is introduced. These methods are based on the methods of statistical convergence and lacunary statistical summability for sequences. Analogs of inclusion and consistency theorems for the sequential methods are established, along with examples, and a Cauchy criteria is given.