Genelleştirilmiş limitler ve istatistiksel yakınsaklık
Generalized limits and statistical convergence
- Tez No: 392693
- Danışmanlar: PROF. DR. CİHAN ORHAN
- Tez Türü: Doktora
- Konular: Matematik, Mathematics
- Anahtar Kelimeler: Banach limitleri, İstatistiksel yakınsaklık, Banach limits, Statistical convergence
- Yıl: 2015
- Dil: Türkçe
- Üniversite: Ankara Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Matematik Ana Bilim Dalı
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: Belirtilmemiş.
Özet
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Özet (Çeviri)
This thesis consists of six chapters. The first chapter is devoted to the introduction. In the second chapter, some deffinitions and theorems concerning the generalized limits and statistical convergence have been given. The original results of this thesis are included in the third, fourth and fifth chapters. It is known that the space of all almost convergent sequences can be represented as the set of all bounded real sequences which have the same value under any Banach limit. Freedman has shown that the space of strongly Cesàro summable bounded sequences can be represented as the set of all bounded real sequences which have the same value under any nonnegative, regular, linear functional L on m for which L(E) = 0 whenever E is a set of natural density zero and E is the character- istic function of E. It is known that strong Cesàro summability and statistical convergence are equivalent on bounded sequences. Hence Freedman has given a rep- resentation for statistical convergence on bounded sequences by such functionals. In the third chapter, we call such functionals S-limits and the relationship between S- limits and Banach limits have been investigated. Some regular sublinear functionals that generate as well as dominate S-limits have also been provided. In the fourth chapter, the definiton of S-limits and Banach limits have been extended to SA-limits and A-Banach limits for a nonnegative regular matrix. Similar questions have also been considered for these concepts. In the fifth chapter some sublinear functionals have been defined and some properties of these functionals have been examined. Some inequalites have also been examined. Finally, the last chapter is devoted to the analysis of the results obtained.
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