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Abstract and Applied Analysis
Volume 2014, Article ID 137468, 7 pages
http://dx.doi.org/10.1155/2014/137468
Research Article

A Linear Functional Equation of Third Order Associated with the Fibonacci Numbers

1Mathematics Section, College of Science and Technology, Hongik University, Sejong 339-701, Republic of Korea
2Department of Mathematics, ETH-Zürich, Ramistraße 101, 8092 Zürich, Switzerland

Received 7 February 2014; Revised 12 June 2014; Accepted 16 June 2014; Published 30 June 2014

Academic Editor: Jesús G. Falset

Copyright © 2014 Soon-Mo Jung and Michael Th. Rassias. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [16 citations]

The following is the list of published articles that have cited the current article.

  • Liviu Cădariu, “Generalized Ulam-Hyers stability results: A fixed point approach,” Springer Optimization and Its Applications, vol. 96, pp. 101–111, 2014. View at Publisher · View at Google Scholar
  • Cristinel Mortici, Michael Th. Rassias, and Soon-Mo Jung, “On the Stability of a Functional Equation Associated with the Fibonacci Numbers,” Abstract and Applied Analysis, vol. 2014, pp. 1–6, 2014. View at Publisher · View at Google Scholar
  • Yeol Je Cho, Choonkil Park, Themistocles M. Rassias, and Reza Saadatipp. 1–343, 2015. View at Publisher · View at Google Scholar
  • Laura Găvruţa, and Paşc Găvruţa, “Approximation of Functions by Additive and by Quadratic Mappings,” Mathematical Analysis, Approximation Theory and Their Applications, vol. 111, pp. 281–292, 2016. View at Publisher · View at Google Scholar
  • Zhan-Peng Yang, Tian-Zhou Xu, and Min Qi, “Ulam-Hyers Stability for Fractional Differential Equations in Quaternionic Analysis,” Advances In Applied Clifford Algebras, vol. 26, no. 1, pp. 469–478, 2016. View at Publisher · View at Google Scholar
  • N. Salehi, and S. M. S. Modarres, “A fixed point method for the stability of a maximum preserving quadratic functional equation in Banach lattices,” Journal of Fixed Point Theory and Applications, 2017. View at Publisher · View at Google Scholar
  • Janusz Brzdęk, Erdal Karapınar, and Adrian Petruşel, “A fixed point theorem and the Ulam stability in generalized dq-metric spaces,” Journal of Mathematical Analysis and Applications, 2018. View at Publisher · View at Google Scholar
  • Hassan Azadi Kenary, and Themistocles M. Rassias, “NAN-RN Approximately Generalized Additive Functional Equations,” Applications of Nonlinear Analysis, vol. 134, pp. 483–506, 2018. View at Publisher · View at Google Scholar
  • Hassan Azadi Kenary, and Themistocles M. Rassias, “On the HUR-Stability of Quadratic Functional Equations in Fuzzy Banach Spaces,” Applications of Nonlinear Analysis, vol. 134, pp. 507–522, 2018. View at Publisher · View at Google Scholar
  • Janusz Brzdȩk, El-sayed El-hady, and Zbigniew Leśniak, “On fixed points of a linear operator of polynomial form of order 3,” Journal of Fixed Point Theory and Applications, vol. 20, no. 2, 2018. View at Publisher · View at Google Scholar
  • Soon-Mo Jung, Michael Th. Rassias, and Yang-Hi Lee, “Uniqueness theorems on functional inequalities concerning cubic-quadratic-additive equation,” Journal of Mathematical Inequalities, vol. 12, no. 1, pp. 43–61, 2018. View at Publisher · View at Google Scholar
  • Janusz Brzdęk, El-sayed El-hady, and Zbigniew Leśniak, “Fixed-point theorem in classes of function with values in a dq-metric space,” Journal of Fixed Point Theory and Applications, vol. 20, no. 4, 2018. View at Publisher · View at Google Scholar
  • Sandra Pinelas, V. Govindan, and K. Tamilvanan, “Stability of a quartic functional equation,” Journal of Fixed Point Theory and Applications, vol. 20, no. 4, 2018. View at Publisher · View at Google Scholar
  • Janusz Brzdęk, and Krzysztof Ciepliński, “A fixed point theorem in n-Banach spaces and Ulam stability,” Journal of Mathematical Analysis and Applications, 2018. View at Publisher · View at Google Scholar
  • Iz-Iddine El-Fassi, “Some new results on hyperstability of the general linear equation in (2, β)-Banach spaces,” Communications of the Korean Mathematical Society, vol. 33, no. 3, pp. 901–917, 2018. View at Publisher · View at Google Scholar
  • Hassan Azadi Kenary, “Fixed Point and Nearly m-Dimensional Euler–Lagrange-Type Additive Mappings,” Springer Optimization and Its Applications, vol. 131, pp. 235–249, 2018. View at Publisher · View at Google Scholar