Inner product quasilinear spaces and some generalizations

This study which is entitled "Inner Product Quasilinear Spaces and Some Generalizations" contains five chapters. In the first chapter, the necessary knowledge about development of quasilinear spaces, usage areas and an example of quasilinear spaces are given. In the second chapter, some basic definitions and theorems which are used in the following chapters, are given. In the third chapter, quasilinear spaces, normed quasilinear spaces, Ω−space and quasilinear operators are introduced. Also some basic theorems and results which are related to these spaces are given. The fourth and fifth chapters are original parts of this study. In the fourth chapter, the concept of inner product quasilinear spaces which are generalization of the inner product spaces and Hilbert quasilinear spaces are defined. Furthermore, in this chapter deals with the some new definitions, theorems and results which are concerned with inner product quasilinear spaces. In addition, orthogonal and orthonormal systems in quasilinear spaces and some new properties of Hilbert quasilinear spaces are examined. Also, quasilinear counterpart of some theorems in linear spaces, are given. In the last chapter, IRn interval spaces and Is, Il∞, Ic, Ic0, Il2 interval sequences spaces which are another examples of the quasilinear spaces are introduced. Furthermore, some algebraic studies on these spaces are given.