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

Liviu Cădariu () and Viorel Radu ()
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Liviu Cădariu: “Politehnica” University of Timişoara
Viorel Radu: West University of Timişoara

Chapter Chapter 3 in Functional Equations in Mathematical Analysis, 2011, pp 19-32 from Springer

Abstract: 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.

Keywords: Additive Cauchy functional equation; Fixed points; Stability; Generalized contractions (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-1-4614-0055-4_3

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