İstatistiksel relative düzgün yakınsaklık ve Korovkin tipi teoremler
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Tarih
2019
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Sinop Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Bu doktora tezinde A- istatistiksel relative düzgün yakınsaklık ve istatistiksel relative equal yakınsaklık kavramları kullanılmıştır. Bu tezde ilk olarak kullanılacak olan bazı tanım, teoremler verilmiştir. Bulgular bölümünün birinci kısmında A-istatistiksel relative düzgün yakınsaklık kavramı double diziler için tanıtılmış ve bu yakınsaklık türü aracılığı ile Korovkin tipi yaklaşım teoremi çalışılmıştır. Burada verilen örnek ile elde edilen sonucun düzgün yakınsaklık ve istatistiksel düzgün yakınsaklıktan daha kuvvetli olduğu gösterilmiştir. Son olarak bu teorem için A-istatistiksel relative düzgün yakınsaklık oranı hesaplanmıştır. İkinci kısımda, istatistiksel relative equal yakınsaklık kavramı tanıtılarak bu kavram yardımıyla Korovkin tipi yaklaşım teoremi elde edilmiştir. Daha sonra yeni elde ettiğimiz teoremin koşullarını sağlayan fakat istatistiksel ve istatistiksel relative Korovkin tipi teoremlerin şartlarını sağlamayan bir örnek sunulmuştur. Sonrasında istatistiksel relative equal yakınsaklık oranı hesaplanmıştır. Bulgular bölümünün son kısmında ise, double diziler için istatistiksel relative equal yakınsaklık tanımı ve Korovkin tipi yaklaşım teoremi verilmiştir. Sonrasında bu yeni tip yaklaşımı sağlayan bir örnek çalışılmıştır. Son olarak bu teorem için istatistiksel relative equal yakınsaklık oranı hesaplanmıştır. Ayrıca Voronovskaya tipi teorem çalışılmıştır.
In this doctoral thesis, the concepts of A-statistical relative uniform convergence and statistical relative equal convergence have been used. In this thesis, firstly some definitions and theorems used in the thesis have been given. In the first part of the findings section, the concept of A-statistical relative uniform convergence has been presented for double sequences and via this type of convergence, Korovkin type approximation theorem has been studied. Then, an example, showing that the result obtained has been stronger than uniform convergence and statistical uniform convergence, is given. Finally the rate of A-statistical relative uniform convergence for this theorem has been computed. In the second part, introducing statistical relative equal convergence, a Korovkin type approximation theorem has been obtained via this type of definition. Also, an example which satisfies the conditions of this theorem but does not provide the conditions of the statistical relative Korovkin type theorems, given previously, has been presented. Then, the rate of statistical relative equal convergence has been computed. In the last part of the findings section, for double sequences the concept of statistical relative equal convergence and Korovkin type approximation theorem have been given. After then, an example satisfying this new type approximation has been studied. Finally the rate of statistical relative equal convergence for this theorem has been computed. Also, Voronovskaya type theorem has been studied.
In this doctoral thesis, the concepts of A-statistical relative uniform convergence and statistical relative equal convergence have been used. In this thesis, firstly some definitions and theorems used in the thesis have been given. In the first part of the findings section, the concept of A-statistical relative uniform convergence has been presented for double sequences and via this type of convergence, Korovkin type approximation theorem has been studied. Then, an example, showing that the result obtained has been stronger than uniform convergence and statistical uniform convergence, is given. Finally the rate of A-statistical relative uniform convergence for this theorem has been computed. In the second part, introducing statistical relative equal convergence, a Korovkin type approximation theorem has been obtained via this type of definition. Also, an example which satisfies the conditions of this theorem but does not provide the conditions of the statistical relative Korovkin type theorems, given previously, has been presented. Then, the rate of statistical relative equal convergence has been computed. In the last part of the findings section, for double sequences the concept of statistical relative equal convergence and Korovkin type approximation theorem have been given. After then, an example satisfying this new type approximation has been studied. Finally the rate of statistical relative equal convergence for this theorem has been computed. Also, Voronovskaya type theorem has been studied.
Açıklama
Anahtar Kelimeler
Matematik, Mathematics
