On algebraic and topological structure of some quasilinear function spaces

This master thesis consists of four parts.In the first part of the thesis, brief information was given about the subjects mentioned in the thesis. Then, what was done in the thesis was mentioned. In the second part, the basic concepts, definitions and theorems used in the following chapters are given. In the third chapter, the definition of quasiliner spaces, which is the generalization of linear spaces, is given. Important algebraic expressions, definitions and theorems in linear spaces are given in quasilinear spaces. In the fourth chapter, the space quasilinear space formed by interval-valued functions is mentioned. It was stated that the other name of this space is the interval valued finite energy signals space. It was also stated that this space is a Hilbert quasilinear space with the norm on it. In addition, a method for estimating the energies of non-deterministic signals with some missing information was developed. Then, it was tried to predict Fourier Transforms in some non-deterministic signals.Here, the previously known Set-valued Fourier Transform was used. For this, inner product quasilinear spaces are used.