Jang, Sun; Park, Choonkil; Cho, Young Hyers-Ulam stability of a generalized additive set-valued functional equation. (English) Zbl 1282.39030 J. Inequal. Appl. 2013, Paper No. 101, 6 p. (2013). Summary: We define a generalized additive set-valued functional equation, which is related to the following generalized additive functional equation: \[ f(x_1+\dots+x_l)=(l-1)f\left(\frac{x_1 + \dots+x_{l-1}}{l-1}\right)+f(x_l) \] for a fixed integer \(l\) with \(l > 1\), and prove the Hyers-Ulam stability of the generalized additive set-valued functional equation. Cited in 5 Documents MSC: 39B82 Stability, separation, extension, and related topics for functional equations 39B55 Orthogonal additivity and other conditional functional equations Keywords:Hyers-Ulam stability; generalized additive set-valued functional equation; closed set; convex set; cone PDFBibTeX XMLCite \textit{S. Jang} et al., J. Inequal. Appl. 2013, Paper No. 101, 6 p. (2013; Zbl 1282.39030) Full Text: DOI References: [1] doi:10.1016/0022-247X(65)90049-1 · Zbl 0163.06301 · doi:10.1016/0022-247X(65)90049-1 [2] doi:10.2307/1907353 · Zbl 0055.38007 · doi:10.2307/1907353 [3] doi:10.2307/1907777 · Zbl 0095.34302 · doi:10.2307/1907777 [4] doi:10.1073/pnas.27.4.222 · Zbl 0061.26403 · doi:10.1073/pnas.27.4.222 [5] doi:10.2969/jmsj/00210064 · Zbl 0040.35501 · doi:10.2969/jmsj/00210064 [6] doi:10.1090/S0002-9939-1978-0507327-1 · doi:10.1090/S0002-9939-1978-0507327-1 [7] doi:10.1006/jmaa.1994.1211 · Zbl 0818.46043 · doi:10.1006/jmaa.1994.1211 [8] doi:10.1016/j.aml.2010.05.011 · Zbl 1204.39028 · doi:10.1016/j.aml.2010.05.011 [9] doi:10.1016/j.jmaa.2004.03.026 · Zbl 1066.46037 · doi:10.1016/j.jmaa.2004.03.026 [10] doi:10.1016/j.aml.2011.02.024 · Zbl 1220.39030 · doi:10.1016/j.aml.2011.02.024 [11] doi:10.1016/j.aml.2011.05.017 · Zbl 1236.39034 · doi:10.1016/j.aml.2011.05.017 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.