Abstract
We present some observations concerning stability of the following linear functional equation (in single variable)
in the class of functions φ mapping a nonempty set S into a Banach space X over a field \(\mathbb{K}\in \{\mathbb{R},\mathbb{C}\}\), where m is a fixed positive integer and the functions f:S→S, F:S→X and \(a_{i}:S\to\mathbb{K}\), i=1,…,m, are given. Those observations complement the results in our earlier paper (Brzdȩk et al. in J. Math. Anal. Appl. 373:680–689, 2011).
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Mathematics Subject Classification
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Dedicated to Professor Themistocles M. Rassias on the occasion of his 60th birthday.
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Brzdȩk, J., Popa, D., Xu, B. (2012). Remarks on Stability of the Linear Functional Equation in Single Variable. In: Pardalos, P., Georgiev, P., Srivastava, H. (eds) Nonlinear Analysis. Springer Optimization and Its Applications, vol 68. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3498-6_7
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