On a new generalization of Fibonacci hybrid numbers

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TAN E., Ait-Amrane N. R.

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, cilt.54, sa.2, ss.428-438, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 54 Sayı: 2
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1007/s13226-022-00264-3
  • Dergi Adı: INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, zbMATH
  • Sayfa Sayıları: ss.428-438
  • Anahtar Kelimeler: Fibonacci sequence, Bi-periodic Horadam sequence, Horadam hybrid number, Hybrid number
  • Ankara Üniversitesi Adresli: Evet

Özet

The hybrid numbers were introduced by Ozdemir [9] as a new generalization of complex, dual, and hyperbolic numbers. A hybrid number is defined by k = a + bi + cc + dh, where a, b, c, d are real numbers and i, epsilon, h are operators such that i(2) = -1, epsilon(2) = 0, h(2) = 1 and ih = -hi = epsilon + i. This work is intended as an attempt to introduce the bi-periodic Horadam hybrid numbers which generalize the classical Horadam hybrid numbers. We give the generating function, the Binet formula, and some basic properties of these new hybrid numbers. Also, we investigate some relationships between generalized bi-periodic Fibonacci hybrid numbers and generalized bi-periodic Lucas hybrid numbers.