Rough statistical convergence on triple sequence of the Bernstein operator of random variables in probability
Küçük Resim Yok
Tarih
2019
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Prince of Songkla University
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
This paper aims to improve further on the work of Phu (2001), Aytar (2008), and Ghosal (2013). We propose a new apporach to extend the application area of rough statistical convergence usually used in triple sequence of the Bernstein operator of real numbers to the theory of probability distributions. The introduction of this concept in the probability of Bernstein polynomials of rough statistical convergence, Bernstein polynomials of rough strong Cesàro summable, Bernstein polynomials of rough lacunary statistical convergence, Bernstein polynomials of rough N? convergence, Bernstein polynomials of rough statistical convergence, and Bernstein polynomials of rough strong (V, ?)summable to generalize the convergence analysis to accommodate any form of distribution of random variables. Among these six concepts in probability only three convergences are distinct Bernstein polynomials of rough statistical convergence: (1) Bernstein polynomials of rough lacunary statistical convergence, (2) Bernstein polynomials of rough statistical convergence where Bernstein polynomials of rough strong Cesàro summable is equivalent to Bernstein polynomials of rough statistical convergence, and (3) Bernstein polynomials of rough N?-convergence which is equivalent to Bernstein polynomials of rough lacunary statistical convergence. Bernstein polynomials of rough strong (V, ?)-summable is equivalent to Bernstein polynomials of rough ? statistical convergence. Basic properties and interrelations of these three distinct convergences are investigated and some observations were made in these classes and in this way we demonstrated that rough statistical convergence in probability is the more generalized concept than the usual Bernstein polynomials of rough statistical convergence. © 2019, Prince of Songkla University. All rights reserved.
Açıklama
Anahtar Kelimeler
Bernstein polynomials, Rough lacunary statistical convergence, Rough n?-convergence, Rough statistical convergence, Rough strong (v,?)- summable, Rough strong cesàro summable, Rough ?- statistical convergence
Kaynak
Songklanakarin Journal of Science and Technology
WoS Q Değeri
Scopus Q Değeri
Q3
Cilt
41
Sayı
3
