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A General Fixed Point Method for the Stability of Cauchy Functional Equation

In: Functional Equations in Mathematical Analysis

Author

Listed:
  • Liviu Cădariu

    (“Politehnica” University of Timişoara)

  • Viorel Radu

    (West University of Timişoara)

Abstract

In this note, we extend the ideas in [12] to obtain some general stability results for additive Cauchy functional equations in β-normed spaces. It is worth noting that two fixed point alternatives together with the error estimations for generalized contractions of type Bianchini–Grandolfi and Matkowski are pointed out, and then used as fundamental tools. Some examples which emphasize the very general hypotheses, are also given.

Suggested Citation

  • Liviu Cădariu & Viorel Radu, 2011. "A General Fixed Point Method for the Stability of Cauchy Functional Equation," Springer Optimization and Its Applications, in: Themistocles M. Rassias & Janusz Brzdek (ed.), Functional Equations in Mathematical Analysis, chapter 0, pages 19-32, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-0055-4_3
    DOI: 10.1007/978-1-4614-0055-4_3
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    Cited by:

    1. Brzdȩk, Janusz & Cădariu, Liviu, 2016. "Stability for a family of equations generalizing the equation of p-Wright affine functions," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 158-171.

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