A new sequence space defined by fractional difference operator and its geometrical properties

This thesis consists of five chapters. In the introduction, a brief information about the historical development of the subject is given. In the material and method section, some definitions and theorems that form the basis of our work, the properties of the fractional difference operator and modular spaces are explained. In the third chapter, some geometric properties which we will need in our study are given. In the fourth section in which we present our findings, we first define our sequence space. After then, by investigating the modular structure of this space, we show that it provides the H-property, k nearly uniform convexity and the uniform Opial property and so we give relevant results. In the last part, suggestions have been made about the contribution of our results to the literatüre and whether more studies can be considered by using these results.