Convergence of m-th order and some new sequence spaces

This thesis consists of six main chapters. In chapter one; we introduced the basic definitions, theorems and some inequalities which we used in our thesis. In chapter two; we introduced classical sequence spaces and examined literature data. In chapter three; we defined the $\lambda^m$-convergence and $\lambda^m$-boundedness. We also examined the relationship between of the ordinary convergence and ordinary boundedness of them. We defined the non-absolute type sequence spaces and examined some topological properties of these spaces. In chapter four; we introduced the some inclusion relations between of the these spaces and also investigated inclusion relations between of these spaces and other defined sequence spaces given previously in literature. In chapter five; we determined the alpha-, beta- and gamma- duals of these spaces. In chapter six; we characterized some matrix classifications of the spaces which we defined into some classical sequence spaces.