Geometric Cesàro sequence spaces and some properties

This thesis consists of four chapters. In the first chapter, the information about the historical background of the subject is given. In the second chapter, the basic definitions and theorems related to the study are handled. The third chapter, which deals with the thesis topic, consists of two parts. In the first part, the definitions of Cesàro sequence spaces with 1≤p<∞ and p=∞ are given in the sense of geometric calculus, which differs from the classical calculus introduced by Newton and Leibnitz, and it is shown that CespG geometric Cesàro sequence spaces are vector spaces, normed spaces, and Banach spaces in the sense of geometric calculus. In addition to, the inclusion relations between the geometric Cesàro sequence space and lpG geometric sequence spaces are researched and some necessary examples are given. In the second part, CesG(p) generalized geometric Cesàro sequence spaces are defined and the basic properties of these spaces are given. Moreover, G-modular, properties of G-modular and their relationship with Luxemburg G-norm are examined. In the last chapter, conclusions and evaluations related to the thesis subject are given.