Generalized ideal convergence

In this study I-convergence of number sequences and related fundamental properties are examined.This thesis consists of five parts.In the first chapter, the historical development of statistical and ideal convergence is given. In the second chapter some basic properties of ideal convergence are given.In the third chapter, for a sequence x=(xn) with real or complex entries, the concepts I-liminf x and I-limsup x are given and some related basic properties are examined.In the fourth chapter, I-convergence of difference sequences and in the fifth chapter the concepts AI -statistical convergence and ideal A- summability are examined.Key words: statistical convergence, ideal convergence, difference sequence.