Asymptotically J-Lacunary statistical equivalent of order alpha for sequences of sets
Yükleniyor...
Tarih
2017
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Int Scientific Research Publications
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
This paper presents the following definition which is a natural combination of the definition for asymptotically equivalent of order alpha, where 0 < alpha <= 1, I-statistically limit, and I-lacunary statistical convergence for sequences of sets. Let (X, rho) be a metric space and theta be a lacunary sequence. For any non-empty closed subsets A(k), B-k subset of X such that d(x, A(k)) > 0 and d(x, B-k) > 0 for each x is an element of X, we say that the sequences {A(k)} and {B-k} are Wijsman asymptotically I-lacunary statistical equivalent of order alpha to multiple L, where 0 < alpha <= 1, provided that for each epsilon > 0 and each x is an element of X, {r is an element of N : 1/h(r)(alpha)|{k is an element of I-r : |d(x; A(k),B-k)- L| >= (sic) }| >= delta} is an element of I, (denoted by {A(k)} (s theta L(Iw)alpha) similar to {B-k}) and simply asymptotically I-lacunary statistical equivalent of order alpha if L = 1. In addition, we shall also present some inclusion theorems. The study leaves some interesting open problems. (C) 2017 All rights reserved.
Açıklama
Anahtar Kelimeler
Asymptotical equivalent, sequences of sets, ideal convergence, Wijsman convergence, I-statistical convergence, I-lacunary statistical convergence, statistical convergence of order alpha
Kaynak
Journal of Nonlinear Sciences and Applications
WoS Q Değeri
N/A
Scopus Q Değeri
Cilt
10
Sayı
6
