Abstract
Applying the classical Banach fixed point theorem we prove that a set-valued function satisfying a general linear functional inclusion admits a unique selection fulfilling the corresponding functional equation. We also adopt the method of the proof for investigating the Rassias stability of general linear equation.
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Smajdor, A., Szczawińska, J. Selections of set-valued functions satisfying the general linear inclusion. J. Fixed Point Theory Appl. 18, 133–145 (2016). https://doi.org/10.1007/s11784-015-0265-9
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DOI: https://doi.org/10.1007/s11784-015-0265-9