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In 1940 (and 1964) S. M. Ulam proposed the well-known Ulam stability problem. In 1941 D. H. Hyers solved the Hyers-Ulam problem for lin- ear mappings. In 1992 and 2008, J. M. Rassias introduced the Euler-Lagrange quadratic mappings and the JMRassias \product-sum" stability, respectively. In this paper we introduce an Euler-Lagrange type quadratic functional equa- tion and investigate the JMRassias \product-sum" stability of this equation. The stability results have applications in Mathematical Statistics, Stochastic Analysis and Psychology.

J. M. RASSIAS PRODUCT-SUM STABILITY OF AN EULER-LAGRANGE FUNCTIONAL EQUATION