Infinite Systems of Differential Equations in Banach Spaces Constructed by Fibonacci Numbers

Merve İlkhan () and Emrah Evren Kara ()
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Merve İlkhan: Düzce University, Department of Mathematics
Emrah Evren Kara: Düzce University, Department of Mathematics

A chapter in Advances in Summability and Approximation Theory, 2018, pp 71-80 from Springer

Abstract: Abstract In the present paper, we investigate the existence theorem for the Cauchy problem $$ x^{^{\prime }}=g(t,x),\quad x(0)=x_{0} $$ in some Banach spaces derived by Fibonacci numbers. For this purpose, we use the Hausdorff measure of noncompactness. Also, we give an example of infinite system of differential equations which has a solution in these spaces but has no solution in the classical Banach sequence spaces $$c_{0}$$ and $$\ell _{p}$$ .

Keywords: Differential equations; Fibonacci numbers; Banach spaces; Hausdorff measure of noncompactness; 34A34; 11B39; 34G20 (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-13-3077-3_4

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DOI: 10.1007/978-981-13-3077-3_4

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