On some k-generalized hypercomplex numbers

In this thesis, the relationships between k-generalized Fibonacci, k-generalized Lucas, k-generalized Pell and k-generalized Pell-Lucas number sequences and hypercomplex numbers are examined. In the first chapter, a literature review related to the thesis topic and the fundamental definitions and theorems utilized in this thesis study are presented. In the second chapter, k-generalized Fibonacci and k-generalized Lucas hypercomplex numbers are defined, and their Binet formulas, as well as the identities between them, are presented. In the third chapter, k-generalized Pell and k-generalized Pell-Lucas hypercomplex numbers are defined. Subsequently, the Binet formulas of these number sequences are given, and the relationships between the two numbers are demonstrated. In the final chapter, which is the fourth chapter, the results of the thesis study are presented.