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

  • Merve İlkhan
  • Emrah Evren KaraEmail author
Chapter

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 

2010 Mathematics Subject Classification

34A34 11B39 34G20 

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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of MathematicsDüzce UniversityDuzceTurkey

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