Complex Fibonacci P-numbers and Fibonacci-P quaternions

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Thesis Type: Doctorate

Institution Of The Thesis: Gazi Üniversitesi, Fen Bilimleri Enstitüsü, Turkey

Approval Date: 2014

Student: NAZMİYE FEYZA YALÇIN

Supervisor: DURSUN TAŞCI

Abstract:

In this study firstly, the complex Fibonacci numbers are generalized to complex Fibonacci p-numbers by using p+1th order recurrence relations. Moreover, some properties are given for these numbers and some results are obtained by choosing the initial conditions pursuant to Lucas p-sequence. Then, an extension of complex Fibonacci p-numbers is examined. In the last part of the study, Fibonacci-p quaternions, which is an extension of complex Fibonacci p-numbers, are defined and the norm of this quaternion is computed.