Let us define () r ij A H a = = to be n n × r-Hankel matrix. The entries of matrix A are 2 n i j F F + − = or 2 n i j L F + − = where n F and n L denote the usual Fibonacci and Lucas numbers, respectively. Then, we obtained upper and lower bounds for the spectral norm of matrix A. We compared our bounds with exact value of matrix A's spectral norm. These kinds of matrices have connections with signal and image processing, time series analysis and many other problems.

In this paper, we have studied the generalized Complex k-Horadam and generalized Gaussian k-Horadam sequences. We have given the generating functions and Binet formulas of generalized Complex k-Horadam and generalized Gaussian k-Horadam sequences. Moreover, we have obtained some important identities involving the generalized Complex k-Horadam and generalized Gaussian k-Horadam numbers.

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In this paper, we have studied and examined the periodicity of solutions of rational difference equation system. Then we obtained equilibrium points of this difference equation system and investigated the behaviour of this system related to equilibrium points.

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