Asymptotically statistical equivalent sequences

ABSTRACTM.Sc. ThesisASYMPTOTICALLY STATISTICAL EQUIVALENT SEQUENCESBekir SOYTÜRKAfyon Kocatepe UniversityGraduate School of Natural and Applied SciencesBasic Science Subdavision of MathematicsSupervisor: Prof. Dr. Fatih NURAYThis thesis consist of five section. First section has been assigned for basicdefinitions and theorems which are necessary. In second part, it has been lookedover the concept of ?λ-statistical convergence? and has been examined therelationship between ?statistical convergence? and ?λ- statistical convergence?with theorems. In third section, has been presented the definition of theasymptotically statistical equivalent which is a natural combination of thedefinition for Asyptotically equivalnet and statistically limit, and has been studiedbasic theorems which is interested in asymptotically statistically. The definition ofSσ,λ-asymptotically equivalnet has been presented in four section and using thisdefinition has been proved Sσ,λ-asymptotically equivalent analogues of λ-statisticalconvergent theorems. In fifth section have been defined the folloving definations,lacunary sequence, lacunary istatistiksel convergence and σ-asiymptoticallylacunary statistical equivalent sequences and using this definition have been alsoproved some inclusion theorems and lacunary istatistiksel convergence and σ-λ- statisticalasiymptotically lacunary statistical equivalent analogues ofconvergent theorems.2007, 57 pagesKeywords: Statistical convergence, λ- statistical convergence, Asymptoticallyequivalent sequences, Asymptotically statistical equivalent sequences, Lacunarystatistical convergence and Asymptotically lacunary statistical equivalentsequences