Fubini polynomials and some properties

This thesis consists of six chapters. The first chapter is reserved for the introduction. In the second chapter, some definitions and lemmas that will be used in other chapters are given. In the third chapter, information about the types of Fubini polynomials is given. Some properties of these polynomials are given. In the fourth chapter, generalized Fubini polynomials are introduced, sum formulas and generating function relations for generalized Fubini polynomials are obtained. In addition, theorems giving the multilinear and multilateral generating functions of this polynomial are obtained. Applications of these theorems are given. In the fifth chapter, higher order generalized Fubini polynomials with two variables are introduced and their properties are given. The sum formula and the generative function relation for bivariate higher order Fubini polynomials were obtained. Theorems giving the bilinear and bilateral generating functions of this polynomial are obtained and the applications of these theorems are given. Then, some recurrence relations and integral relations of these polynomials are obtained. In the last section, conclusions and recommendations are given.