Tauberian theorems for weighted means of double sequences

This thesis essentially consists of threee chapters. In the first chapter, the historical development of Tauberian theory and brief introduction of summability methods are mentioned, and then previous works on the weighted mean method of single and double sequences and the results obtained in this thesis are included. In the second chapter, firstly basic defitions and theorems with regard to weighted mean method of single sequences are given. Later, concepts related to the weighted mean summability of double sequnces are introduced and Tauberian theorems are demonstrated. In the third chapter, the concept of generator sequence for double sequences is presented and Tauberian theorems are proved by using generator sequences. Key Words: double sequences, the weighted means method of summability, Tauberian theorems, slowly decreasing sequences, slowly oscillating sequnces, generator sequences.