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

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Functional Equations in Mathematical Analysis

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 52))

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.

Mathematics Subject Classification (2000): Primary 39B62,39B72,39B82,47H09

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Author information

Authors and Affiliations

  1. Department of Mathematics, “Politehnica” University of Timişoara, Piaţa Victoriei no. 2, 300006, Timişoara, Romania

    Liviu Cădariu

  2. Faculty of Mathematics and Computer Science, West University of Timişoara, Bv. Vasile Pârvan 4, 300223, Timişoara, Romania

    Viorel Radu

Authors
  1. Liviu Cădariu
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  2. Viorel Radu
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Correspondence to Liviu Cădariu .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, National Technical University of Athens, Iroon Polytechneiou 9, Athens, 15780, Greece

    Themistocles M. Rassias

  2. Institute of Mathematics, Pedagogical University, ul. Podchorazych 2, Krakow, 30-084, Poland

    Janusz Brzdek

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Cădariu, L., Radu, V. (2011). A General Fixed Point Method for the Stability of Cauchy Functional Equation. In: Rassias, T., Brzdek, J. (eds) Functional Equations in Mathematical Analysis. Springer Optimization and Its Applications(), vol 52. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0055-4_3

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