Some generalized statistical derivatives

This study includes some new concepts and theorems related to statistical and Cesàro derivatives. The fourth and fifth chapters of this thesis constitute the original part of the study. The first chapter of the study, which includes the concepts and theorems about statistical and Cesàro derivatives, examines the historical development of the subject. It is stated that these concepts first emerged in the 19th century and have been studied by various mathematicians since then. The second chapter deals with basic definitions and theorems related to the subject. Here, information is given about statistical and Cesàro convergence concepts and their variations concerning sequences of numbers. In the third chapter, statistical and Cesàro derivatives, along with related concepts and theorems, are examined. In the fourth chapter, after explaining the relationship between classical and statistical derivatives, the concepts of (V,λ)- derivative and strong (V,λ)- derivative are examined. Also, definitions of λ- statistical derivative of order α, (V,λ)- derivative of order α and strong (V,λ)- derivative of order α are given, and the relationships between these concepts are examined. Finally, with the condition 0<α≤β≤1 the relationship between λ- statistical derivative of order β and strong (V,λ)- derivative of order α is given. In the fifth chapter, after defining deferred statistical derivative, deferred Cesàro derivative and strong deferred Cesàro derivative, some results related to these concepts and the relationships between the created classes are given. Finally, in the sixth chapter, the results obtained in the study are summarized.