Cihan, OrhanDemirci, Kamil2022-04-112022-04-111992http://hdl.handle.net/20.500.12575/78603ABSTRACT 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.trMatris dönüşümlerimasterThesis