Tauberian theorems for double sequences which are statistically ( C, 1, 1 ) summable in fuzzy number space

This study consists of three chapters. The first chapter is introduction chapter. In this chapter historical developments of Tauberian theory and the notion of statistical convergence are mentioned. Studies concerning statistical summability of double sequences are summarized. Also, information about fuzzy set theory are given and the aim of this thesis are introduced. In the second chapter, first, the notion of statistical convergence for double sequence is defined. Next, Tauberian conditions for double sequences that are statistically $(C,1,1)$ summable are given. Finally, basic definitions and theorems related to fuzzy numbers and fuzzy positive linear operators are given. In the third chapter, original results of this thesis are given. In this chapter statistical $(C,1,1)$ summability method for fuzzy double sequences is introduced and Tauberian conditions under which statistical convergence of fuzzy double sequences follows from the statistical $(C,1,1)$ summability are given. Furthermore by means of our new method We prove a Korovkin-type approximation theorem for a double sequence of fuzzy positive linear operators.