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Stability of the Lobacevski equation. (English) Zbl 1206.39024

Summary: The aim of this paper is to investigate the superstability of the Lobachevskii equation \[ f(\frac{x + y}{2})^2 = f(x)f(y), \] which is bounded by the unknown functions \(\varphi (x)\) or \(\varphi (y)\). The obtained result is a generalization of P. Găvrută’s result [in: Stability of mappings of Hyers-Ulam type, 93–98 (1994; Zbl 0844.39007)].

MSC:

39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges

Citations:

Zbl 0844.39007
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