Statistical convergence of number sequences and some generalizations

In this thesis we examine and study statistical convergence, statistical boundedness and some other notions related to these concepts for sequences of real numbers. At the first we give the statistically convergent, statistically Cauchy and statistically bounded sequences of real numbers and then we give limit inferior and limit superior of a sequence. Then we establish the relations between these concepts. After that we study the concept strong p-Cesàro summability of sequences of real numbers. In the last step we give the relationship between the sets of sequences which are statistically convergent of order α, for different α's such that 0< α ≤1. Furthermore, we also give the relationship between the sets of sequences which are strongly p-Cesàro summable of order α for different α's such that α>0. At the end we give and study λ-statistical convergence and λ- statistical convergence of order α for number sequences, where λ =(λn) is non-decreasing sequence of positive number such that λn+1≤λn+1, λ1=1, λn→∞ as n→∞.