On f-statistical convergence and multiplier sequence space

This thesis consists of five chapters. In the first chapter, the importance of the subject and previous studies are mentioned. In the second part, basic definitions and theorems are given. The third part covers the subjects of modulus function and 𝑓−statistical convergence. In the fourth chapter, the definitions and theorems of uniform 𝑓−statistical convergence are given. Also the relationship between 𝑓−statistical convergence and uniform 𝑓−statistical convergence was examined. The fifth chapter, multiplier sequence spaces defined by 𝑓−statistically convergence in the 𝑙∞ sequence space are handled and a new version of the Orlicz-Pettis theorem within the frame of the 𝑓−statistically convergence are given.