Variations on strongly lacunary quasi Cauchy sequences
3rd International Conference on Analysis and Applied Mathematics, ICAAM 2016, Almaty, Kazakistan, 7 - 10 Eylül 2016, cilt.1759, (Tam Metin Bildiri)
- Yayın Türü: Bildiri / Tam Metin Bildiri
- Cilt numarası: 1759
- Doi Numarası: 10.1063/1.4959665
- Basıldığı Şehir: Almaty
- Basıldığı Ülke: Kazakistan
- Anahtar Kelimeler: Continuity, Quasi-Cauchy sequences, Strongly lacunary convergence
- Maltepe Üniversitesi Adresli: Evet
Özet
We introduce a new function space, namely the space of Nθ (p)-ward continuous functions, which turns out to be a closed subspace of the space of continuous functions for each positive integer p. Nθα(p)-ward continuity is also introduced and investigated for any fixed 0 < α ≤ 1, and for any fixed positive integer p. A real valued function f defined on a subset A of R, the set of real numbers is Nθα(p)-ward continuous if it preserves Nθα(p)-quasi-Cauchy sequences, i.e. (f (xn)) is an Nθα(p)-quasi-Cauchy sequence whenever (xn) is Nθα(p)-quasi-Cauchy sequence of points in A, where a sequence (xk) of points in R is called Nθα(p)-quasi-Cauchy if limr→∞1hrα kϵIr| Δxk |p=0, where Δxk = xk+1-xk for each positive integer k, p is a fixed positive integer, α is fixed in] 0, 1], Ir = (kr-1, kr], and θ = (kr) is a lacunary sequence, i.e. an increasing sequence of positive integers such that k0 ≈ 0, and hr: kr-kr-1 →∞.