Abstract
The purpose of the present paper is to investigate the functional equation
where f, g and h are self-mappings of a real interval I and M, N : I 2 → I are functions. In particular, we will show that under appropriate assumptions imposed on the functions M, N the local boundedness of f implies the continuity of g.
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References
Ng C.T.: Local boundedness and continuity for a functional equation on topological spaces. Proc. Am. Math. Soc. 39, 525–529 (1973)
Matkowski J.: Affine and convex functions with respect to the logarithmic mean. Colloq. Math. 95(2), 217–230 (2003)
Pfanzgl J.: On a functional equation related to families of exponential probability measures. Aequationes Math. 4, 139–142 (1970)
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Nowak, A. On affine functions with respect to some means. Aequat. Math. 80, 269–275 (2010). https://doi.org/10.1007/s00010-010-0029-y
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DOI: https://doi.org/10.1007/s00010-010-0029-y