Abstract
In 1940 S. M. Ulam proposed at the University of Wisconsin the problem: "Give conditions in order for a linear mapping near an approximately linear mapping to exist". In 1982-2013, the second author solved the above Ulam problem for a variety of quadratic mappings. Interesting stability results have been achieved by S. A. Mohiuddine et al., since 2009. In this paper, we solve the Ulam stability problem for Euler-Lagrange (alpha, beta; kappa) quadratic mapping. The other authors of this research area have established important results also on functional inequalities.