Abstract
Given a set \(T\subset (0, +\infty )\), a function \(c:T\rightarrow \mathbb R\) and a real number p we study continuous solutions \(\varphi \) of the simultaneous equations
Here \(\varphi \) is defined on an interval \(I\subset (0, +\infty )\), so the equations are postulated on a restricted domain: for any fixed \(t \in T\) we assume that \(x \in I\) is such that \(tx \in I\). In the case when T is large in a sense, we determine the form of \(\varphi \) on a non-trivial subinterval of I. The research is a continuation of that of “non-restricted”, where \(I=(0,+\infty )\), made in Jarczyk (Ann Univ Sci Budapest Sect Comp 40:353–362, 2013).
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Jarczyk, W.: Uniqueness of solutions of simultaneous difference equations. Ann. Univ. Sci. Budapest. Sect. Comp. 40, 353–362 (2013)
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Dedicated to Professor Karol Baron on the occasion of his 70th birthday.
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Jarczyk, W., Pasteczka, P. Simultaneous difference equations on a restricted domain. Aequat. Math. 93, 239–246 (2019). https://doi.org/10.1007/s00010-018-0616-x
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DOI: https://doi.org/10.1007/s00010-018-0616-x