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

Anna Bahyrycz () and Janusz Brzdȩk ()
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Anna Bahyrycz: Pedagogical University
Janusz Brzdȩk: Pedagogical University

A chapter in Handbook of Functional Equations, 2014, pp 37-57 from Springer

Abstract: 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 $\mu,\nu:S^2\to [0,\infty)$ .

Keywords: Hyers-Ulam stability; Square symmetric groupoids; Homomorphism; Fixed point; Complete metric; Linear equation (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4939-1286-5_2

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DOI: 10.1007/978-1-4939-1286-5_2

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