Some generalized statistically convergent sequences spaces

This study consists of five chapters. The first chapter is devoted to the introduction part and in this chapter, the historical development of statistical convergence is given. In the second part, some basic concepts and results related to the subject are given. In the third chapter, we introduce λd – statistical convergence, λd – statistical boundedness and strong (V,λ)d- summability of a sequence in a metric space. Also, for various sequences λ=(λn) in Λ, some inclusion relations are given. Furthermore we establish some inclusion relations between the sets of strongly (V,λ)d- summable sequences for various sequences λ=(λn) in the class Λ*. In the fourth chapter, we introduce d- statistical convergence of order α, d- statistical boundedness of order α and d- strong p- Cesàro summability of order α for sequences in a metric space. Furthermore, we investigate the relations between the sets of sequences which are d- strongly p- Cesàro summable of order α for various values of α's in (0, 1) and we give some inclusion relations for various values of α's in (0, 1]. In the fifth chapter, we give df- statistical convergence and df- statistical boundedness and relations between them with respect to a modulus f for sequences in a metric space. In addition, for some special cases of the f modulus, we give some inclusion relations between the sets of df- strongly Cesàro summable sequences and the relations between the set of df- statistically convergent sequences and the set of df- strongly Cesàro summable sequences. Keywords: Density, Metric space, Modulus function, Statistical convergence, Strong Cesàro summability.