Lacunary statistically upward half quasi-Cauchy sequences


Cakalli H., MUCUK O.

International Conference on Advancements in Mathematical Sciences, AMS 2015, Antalya, Türkiye, 5 - 07 Kasım 2015, cilt.1676, (Tam Metin Bildiri)

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası: 1676
  • Doi Numarası: 10.1063/1.4930439
  • Basıldığı Şehir: Antalya
  • Basıldığı Ülke: Türkiye
  • Anahtar Kelimeler: Continuity, Lacunary statistically convergence, Quasi-Cauchy sequences, Sequences, Series summability
  • Maltepe Üniversitesi Adresli: Evet

Özet

A real valued function defined on a subset E of R, the set of real numbers, is lacunary statistically upward continuous if it preserves lacunary statistically upward half quasi-Cauchy sequences where a sequence (xn) of points in R is called lacunary statistically upward half quasi-Cauchy if [EQUATION PRESENTED] for every ε > 0, and θ = (kr) is an increasing sequence θ = (kr) of non-negative integers such that k0 = 1 and hr: kr-kr-1 → . We investigate lacunary statistically upward continuity, and prove interesting theorems. It turns out that any lacunary statistically upward continuous function on a below bounded subset of R is uniformly continuous.