Some geometric properties of the generalized difference sequence spaces

Some Geometric Properties Of The Generalized Difference Sequence SpacesThis thesis consist of four chapters.In the first chapter, we give some fundamental definitions and theorems.In the second chapter, we give some geometric properties of Banach spaces and relations between these properties.In the third chapter, we define a new difference sequence space by means of the generalized de la Vallee-Poussin mean. Then, we show that the space is paranormed space and modular sequence space. Also, we prove that this space is Banach space equipped with the Luxemburg norm. Later, we study geometric properties of and the spaces which are obtained by special cases of and .In the fourth chapter, we introduce the space by using lacunary sequence and investigate modular structure of this space. Then, we consider the space equipped with the Luxemburg norm and show that it has k-NUC property but is not rotund (strictly convex).Keywords: De la Vallee-Poussin mean, Lacunary sequence, Luxemburg norm, Modular space, Rotundity (strictly convex)