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.