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On Hyperstability of the Cauchy Functional Equation in n -Banach Spaces

Author

Listed:
  • Janusz Brzdęk

    (Faculty of Applied Mathematics, AGH University of Science and Technology, Mickiewicza 30, 30-059 Kraków, Poland)

  • El-sayed El-hady

    (Mathematics Department, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi Arabia
    Basic Science Department, Faculty of Computers and Informatics, Suez Canal University, Ismailia 41522, Egypt)

Abstract

We present some hyperstability results for the well-known additive Cauchy functional equation f ( x + y ) = f ( x ) + f ( y ) in n -normed spaces, which correspond to several analogous outcomes proved for some other spaces. The main tool is a recent fixed-point theorem.

Suggested Citation

  • Janusz Brzdęk & El-sayed El-hady, 2020. "On Hyperstability of the Cauchy Functional Equation in n -Banach Spaces," Mathematics, MDPI, vol. 8(11), pages 1-12, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1886-:d:437608
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    References listed on IDEAS

    as
    1. Soon-Mo Jung & Dorian Popa & Michael Rassias, 2014. "On the stability of the linear functional equation in a single variable on complete metric groups," Journal of Global Optimization, Springer, vol. 59(1), pages 165-171, May.
    2. Tian Zhou Xu & John Michael Rassias, 2012. "On the Hyers-Ulam Stability of a General Mixed Additive and Cubic Functional Equation in n -Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-23, April.
    3. Elhoucien Elqorachi & Michael Th. Rassias, 2018. "Generalized Hyers-Ulam Stability of Trigonometric Functional Equations," Mathematics, MDPI, vol. 6(5), pages 1-11, May.
    4. Hahng-Yun Chu & Ahyoung Kim & Jinhae Park, 2016. "On the Hyers–Ulam stabilities of functional equations on n -Banach spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 289(10), pages 1177-1188, July.
    5. Tian Zhou Xu, 2013. "Approximate Multi-Jensen, Multi-Euler-Lagrange Additive and Quadratic Mappings in -Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, September.
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