A-statistical convergence with a rate

This Ph.D. thesis consists of five chapters. The first chapter is devoted to the introduction. The original results of this thesis are included in the second, third and fourth chapters. In the first part of the second chapter, some definitions and theorems have been given. In the second part of the second chapter, the concept of A-density with the rate of o(a_{n}) is defined and certain properties are examined. In the next part, A-strong convergence with the rate of o(a_{n}) via A-statistical convergence with the rate of o(a_{n}) has been characterized. In the last part, some criteria for A-statistical convergence with the rate of o(a_{n}) have been obtained. In the third chapter, the summability of spliced sequences has been studied and the A-limit with the rate of o(a_{n}) of spliced sequences may be expressed as a linear combination of A-densities with the rate of o(a_{n}) of the sets in the partition. Finally, the last chapter is devoted to the analysis of the results obtained in the thesis.