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Handbook of Functional Equations pp 37–57Cite as

Remarks on Stability of the Equation of Homomorphism for Square Symmetric Groupoids

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Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 96))

Abstract

Let \((G,\star)\) and \((H,\circ)\) be square symmetric groupoids and \(S\subset G\) be nonempty. We present some remarks on stability of the following conditional equation of homomorphism

$$f(x\star y)=f(x)\circ f(y) \qquad x,y\in S, x\star y\in S\;,$$

in the class of functions mapping S into H. In particular, we consider the situation where \(H=\mathbb{R}\) and

$$-\nu(x,y)\le h(x\star y)-h(x)\circ h(y) \le \mu(x,y) \qquad x,y\in S, x\star y\in S\;,$$

with some functions \(\mu,\nu:S^2\to [0,\infty)\).

Mathematics Subject Classification (2010) 39B22, 39B52, 39B82.

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Authors and Affiliations

  1. Department of Mathematics, Pedagogical University, Podchora¸żych 2, 30-084, Kraków, Poland

    Anna Bahyrycz & Janusz Brzdȩk

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  1. Anna Bahyrycz
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  2. Janusz Brzdȩk
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Correspondence to Anna Bahyrycz .

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  1. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

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Bahyrycz, A., Brzdȩk, J. (2014). Remarks on Stability of the Equation of Homomorphism for Square Symmetric Groupoids. In: Rassias, T. (eds) Handbook of Functional Equations. Springer Optimization and Its Applications, vol 96. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1286-5_2

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