Statistical convergence of order α in double sequences with respect to a modulus function

This study consists of four chapters. In Chapter 1, we give some informations about the importance and historical development of statistical convergence. In Chapter 2, we give some fundamental definitions and theorems. In Chapter 3, we examine the concepts of f density of order α and statistical convergence order α with respect to a modulus function f of double sequences. We define f strongly p-Cesàro summable sequence spaces of order α in double sequences and examine some relations between these sequence spaces under condition lim_{t→∞}((f(t))/t)>0, where f is any modulus. Moreover, we examine some inclusion relations between f statistical convergence of order α in double sequences of a modulus function and strongly p-Cesàro summable sequences in double sequences under some conditions. In Chapter 4, we examine some inclusion relations between the concepts uniform density, uniform statistical convergence and uniform strongly p-Cesàro summable sequences of order α for double sequences. We give also some inclusion relations between uniform statistical convergence of order α and uniform strongly p-Cesàro summable of order α for double sequences, where f is any modulus function. Furthermore, we define the concept f uniform density of order α for double sequences and examine inclusion relations for uniform f statistical convergence and uniform strong p-Cesàro summability in double sequences.