On a new generalization of Fibonacci hybrid numbers

Elif Tan () and N. Rosa Ait-Amrane ()
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Elif Tan: Ankara University
N. Rosa Ait-Amrane: Faculty of Mathematics, RECITS Laboratory, USTHB

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 2, 428-438

Abstract: Abstract The hybrid numbers were introduced by Ozdemir [9] as a new generalization of complex, dual, and hyperbolic numbers. A hybrid number is defined by $$k=a+bi+c\epsilon +dh$$ k = a + b i + c ϵ + d h , where a, b, c, d are real numbers and $$ i,\epsilon ,h$$ i , ϵ , h are operators such that $$i^{2}=-1,\epsilon ^{2}=0,h^{2}=1$$ i 2 = - 1 , ϵ 2 = 0 , h 2 = 1 and $$ih=-hi=\epsilon +i$$ i h = - h i = ϵ + 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.

Keywords: Fibonacci sequence; Bi-periodic Horadam sequence; Horadam hybrid number; Hybrid number; 11B39; 05A15; 11K31 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13226-022-00264-3

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