Some classical tauberian theorems and their statistical extensions for Cesàro summable double sequences

This thesis essentially consists of five chapters. In the first chapter, some informations about the late history of (C,1,1) summability method and its Tauberian results with its statistical extensions, that is about the history from the early part of 20th century until these days are given. In the second chapter, some basic concepts with respect to double sequences and the relationship between these concepts are mentioned. In the third chapter, generator sequences and the Kronecker identities for double sequences in certain senses are introduced. The most comprehensive necessary and sufficient conditions and some Tauberian conditions for double sequences that P-convergence follows from the (C,1,1) summability are investigated and also some corollaries related to these conditions are presented. In the fourth chapter, the concept of statistical convergence for double sequences is introduced and various characterizations of this concept are organized. Some Tauberian conditions and necessary and sufficient conditions that P-convergent and statistical convergent sequences follow from statistically (C,1,1) summable double sequences are examined and some corollaries related to these conditions are obtained. In the last chapter, all studies done during the thesis are summarized, it is briefly mentioned the conclusions which reach as a result of this study.