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ON THE SEQUENCES RELATED TO FIBONACCI AND LUCAS NUMBERS
OZGUR NIHAL YILMAZ Korean Mathematical Society 2005 대한수학회지 Vol.42 No.1
In this paper, we obtain some properties of the sequences $U^{q}_n\;and\;V^{q}_n$ introduced in [6]. We find polynomial representations and formulas of them. For q = 5, $U^{5}_n$ is the Fibonacci sequence $F_n\;and\;V^{5}_n$ is the Lucas sequence $L_n$.
SOME FIXED-POINT RESULTS ON PARAMETRIC N<sub>b</sub>-METRIC SPACES
Tas, Nihal,Ozgur, Nihal Yilmaz Korean Mathematical Society 2018 대한수학회논문집 Vol.33 No.3
Our aim is to introduce the notion of a parametric $N_b-metric$ and study some basic properties of parametric $N_b-metric$ spaces. We give some fixed-point results on a complete parametric $N_b-metric$ space. Some illustrative examples are given to show that our results are valid as the generalizations of some known fixed-point results. As an application of this new theory, we prove a fixed-circle theorem on a parametric $N_b-metric$ space.