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Generalised Hyers-Ulam product-sum stability of a Cauchy type additive functional equation. (English) Zbl 1218.39023
Summary: In 1940 (and 1964), {\it S. M. Ulam} [A collection of mathematical problems. (Interscience Tracts in Pure and Applied Mathematics. No. 8.) New York and London: Interscience Publishers (1960; Zbl 0086.24101)] proposed the well-known Ulam stability problem. In 1941, {\it D. H. Hyers} [Proc. Natl. Acad. Sci. USA 27, 222--224 (1941; Zbl 0061.26403; JFM 67.0424.01)] solved the Hyers-Ulam problem for linear mappings. In 2008, {\it K. Ravi, M. Arunkumar} and {\it J. M. Rassias} [Int. J. Math. Stat. 3, No. A08, 36--46 (2008; Zbl 1144.39029)] introduced the generalised Hyers-Ulam “product-sum” stability. In this paper, we introduce a Cauchy type additive functional equation and investigate the generalised Hyers-Ulam “product-sum” stability of this equation.

##### MSC:
 39B82 Stability, separation, extension, and related topics
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