On a Jensen-Hosszú equation. II. (English) Zbl 1382.39030

Kominek, Zygfryd; Sikorska, Justyna

Math. Inequal. Appl. 15, No. 1, 61-67 (2012).

Summary: We solve functional equation of the form \[ f(x + y - xy) + f (xy) = 2f\left(\frac{x+y}{2}\right) \] in the class of functions transforming the unit interval into the space of all reals. We also prove that this equation is stable in the Hyers-Ulam’s sense.
For part I, see [Z. Kominek, Ann. Math. Sil. 23, 57–60 (2009; Zbl 1229.39032)].

MSC:

39B22	Functional equations for real functions
39B82	Stability, separation, extension, and related topics for functional equations

Keywords:

Jensen functional equation; Hosszú functional equation; Hyers-Ulam stability; approximation