In this paper, we introduce multi-Jensen-cubic mappings and unify the system of functional equations defining the multi-Jensen-cubic mapping to a single equation. Applying a fixed point theorem, we establish the generalized Hyers-Ulam stability of multi-Jensen-cubic mappings. As a known outcome, we show that every approximate multi-Jensen-cubic mapping can be multi-Jensen-cubic.
Aoki, Tosio. "On the stability of the linear transformation in Banach spaces." J. Math. Soc. Japan 2 (1950): 64-66.
Bahyrycz, Anna, and Jolanta Olko. "On stability and hyperstability of an equation characterizing multi-Cauchy-Jensen mappings." Results Math. 73, no. 2 (2018): Article 55.
Bahyrycz, Anna, and Krzysztof Cieplinski, and Jolanta Olko. "On an equation characterizing multi-Cauchy-Jensen mappings and its Hyers-Ulam stability." Acta Math. Sci. Ser. B (Engl. Ed.) 35, no. 6 (2015): 1349-1358.
Financed by the National Centre for Research and Development under grant No. SP/I/1/77065/10 by the strategic scientific research and experimental development program:
SYNAT - “Interdisciplinary System for Interactive Scientific and Scientific-Technical Information”.