The Relations Among $k$-Fibonacci, $k$-Lucas, and Generalized $k$-Fibonacci Numbers and the Spectral Norms of the Matrices Involving These Numbers

Abstract

In this study, we obtain the relations among $k$-Fibonacci, $k$-Lucas, and generalized $k$-Fibonacci numbers. Then, we define circulant matrices involving $k$-Lucas and generalized $k$-Fibonacci numbers. Finally, we investigate the upper and lower bounds for the norms of these matrices.