Browsing by Author "Demirci, Kamil"
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Item A-İstatistiksel yakınsaklık ve çarpan uzayları(Fen Bilimleri Enstitüsü, 1998) Demirci, Kamil; Orhan, CihanBu tez beş bölümden oluşmaktadır. Birinci bölümde, tezin çalışma kapsamı anlatılacaktır. İkinci bölümde, yoğunluk, istatistiksel yakınsaklık, istatistiksel üst limit ve alt limit ve istatistiksel çekirdek kavramları hatırlatılmıştır. Tezimizdeki orijinal sonuçlar, Bölüm 3,4 ve 5 de verilmiştir. Üçüncü bölümde, A-yoğunluk ve A-istatistiksel yakınsaklık tanıtılıp, A-istatistiksel üst limit ve alt limit ve A-istatistiksel çekirdek kavramları verilmiştir. Ayrıca çekirdeklerin içerilmesine ilişkin bazı teoremler ispatlanmıştır. Dördüncü bölümde, satırları spread koşulunu gerçekleyen, negatif olmayan regüler bir A matrisi için A-istatistiksel yakınsak diziler uzayının lokal konveks bir FK-topolojisi ile donatılamayacağı gösterilmiştir. Aslında bu sonuç Kline tarafından Doktora tezinde verilmiştir. Fakat burada daha kısa ve alternatif bir ispat verilmiştir. Ayrıca sınırlı A-istatistiksel yakınsak diziler uzayının sınırlı çarpan uzayını oluşturup, "BIN programı" kullanılarak, Fridy ve Miller' e ait bir sonucun benzeri sınırlı çarpanlar için elde edilmiştir. Beşinci bölümde, kuvvetli A-toplanabilme tanımı, bir Orlicz fonksiyonuna göre kuvvetli A-toplanabilme tanımına genişletilip, £n uzayındaki ideal kavramı yardımıyla, A-istatistiksel yakınsaklık, kuvvetli A-toplanabilme ve A2-şartını gerçekleyen bir Orlicz fonksiyonuna göre kuvvetli A-toplanabilmenin sınırlı diziler üzerinde denk olduğu gösterilmiştir. Abstract This thesis consists of five chapters. The first chapter is devoted to the introduction. In the second chapter, density, statistical convergence, statistical limit superior and limit inferior and statistical core have been recalled. The original results in our thesis have been collected in Chapters 3,4 and 5. In the third chapter, using the concept of A-density and A-statistical convergence, the notion of A-statistical limit superior and limit inferior and A- statistical core have been introduced. Furthermore, some theorems regarding the core inclusions have been proved. In the fourth chapter, it is shown that the set of all A-statistically convergent sequences cannot be given a locally convex FK topology where A is a nonnegative regular matrix whose rows spread. Actually this result has been given by Kline in her Ph.D. Thesis. But here, a short and alternate proof of it has been provided. Moreover, the bounded multiplier space of bounded A-statistically convergent sequences are studied; and using "|3IN program", an analogue of a result of Fridy and Miller for bounded multipliers is given. In the last chapter, the definition of strong A-summability has been extended to a definition of strong A-summability with respect to an Orlicz function, via the ideal in.£", it is shown that strong A-summability with respect to an Orlicz function which satisfies A2 -condition and strong A-summability and A-statistical convergence are equivalent on bounded sequences.Item Deferred Nörlund statistical relative uniform convergence and Korovkin-type approximation theorem(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Demirci, Kamil; Dirik, Fadime; Yıldız, Sevda; Other; OtherIn this paper, we define the concept of statistical relative uniform convergence of the deferred Nörlund mean and we prove a general Korovkin-type approximation theorem by using this convergence method. As an application, we use classical Bernstein polynomials for defining an operator that satisfies our new approximation theorem but does not satisfy the theorem given before. Additionally, we estimate the rate of convergence of approximating positive linear operators by means of the modulus of continuity.Item İstatiksel yakınsaklık(Fen Bilimleri Enstitüsü, 1992) Demirci, Kamil; Cihan, Orhan; MatematikABSTRACT Masters Thesis STATISTICAL CONVERGENCE Kâmü DEMİRCİ Ankara University Graduate School of Natural and Applied Sciences Department of Mathematics Supervisor: Assoc. Prof. Dr. Cihan ORHAN 1992, Page: 73 Jury: Assoc. Prof. Dr. CiTian ORHAN Prof. Dr. Öner ÇAKAR Prof. Dr. Zafer NURLU This thesis consits of three chapters. In the first chapter, the notion of statistical convergence, the relationship between this notion and density and statistical Cauchy sequence has been given. Furthermore the relationship between statistical convergence and the strong p-Cesaro summabiltiy has been investigated and some Tauberian theorems for statistical convergence have been given. The topological properties of statistical convergence have also been given in this chapter. In the second chapter, lacunary statistical convergence have been introduced and some inclusion theorems between lacunary statistical convergence and statistical convergence have been studied. Uniqueness of limit for the lacunary statistical convergence, lacunary refinement and a relationship between lacunary statistical convergence and strongly almost convergence have also been investigated. Moreover, Cauchy criteria, Tauberian theorem, summability properties and the matrix charaterization for the lacunary statistical convergence have also been given. In the last chapter, modulus function, strongly A-summability, strongly A-summability with respect to a modulus function and A-statistical convergence have been introduced. Some relationships among the above notions, via the ideal in X, have been studied. oo' KEY WORDS: Matrix transformation, regular matrix, conservative matrix, statistical convergence, density, statistical Cauchy sequence, strongly p-Cearo summability, lacunary statistical convergence, strongly almost convergence, modulus function, strongly A-summability, strongly A-summability with respect to a modulus function, A-statistical convergence.Item On the K_{a}-continuity of real functions(Ankara Üniversitesi Fen Fakültesi, 2020-06-30) Yıldız, Sevda; Demirci, Kamil; Dirik, Fadime; Other; OtherThe aim of the present paper is to define K_{a}-continuity which is associated to the number sequence a=(a_{n}) and to give some new results.