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On the stability of the linear functional equation in a single variable on complete metric groups

Author

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  • Soon-Mo Jung
  • Dorian Popa
  • Michael Rassias

Abstract

In this paper we obtain a result on Hyers–Ulam stability of the linear functional equation in a single variable $$f(\varphi (x))=g(x) \cdot f(x)$$ f ( φ ( x ) ) = g ( x ) · f ( x ) on a complete metric group. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:59:y:2014:i:1:p:165-171
    DOI: 10.1007/s10898-013-0083-9
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    Citations

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    Cited by:

    1. Elhoucien Elqorachi & Michael Th. Rassias, 2018. "Generalized Hyers-Ulam Stability of Trigonometric Functional Equations," Mathematics, MDPI, vol. 6(5), pages 1-11, May.
    2. Jae-Hyeong Bae & Ick-Soon Chang & Hark-Mahn Kim, 2022. "Almost Generalized Derivation on Banach Algebras," Mathematics, MDPI, vol. 10(24), pages 1-8, December.
    3. 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.
    4. Fang Wang & Ying Gao, 2022. "The Analysis of Hyers–Ulam Stability for Heat Equations with Time-Dependent Coefficient," Mathematics, MDPI, vol. 10(22), pages 1-10, November.
    5. Kandhasamy Tamilvanan & Ali H. Alkhaldi & Ravi P. Agarwal & Abdulaziz M. Alanazi, 2023. "Fixed Point Approach: Ulam Stability Results of Functional Equation in Non-Archimedean Fuzzy φ -2-Normed Spaces and Non-Archimedean Banach Spaces," Mathematics, MDPI, vol. 11(2), pages 1-24, January.

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