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On the Hyers-Ulam stability of Pexider-type extension of the Jensen-Hosszu equation. (English) Zbl 1441.39030
Summary: We consider the following pexiderized version of Jensen-Hosszú equation of the form \[ 2f (\frac{x + y}{2}) = g(x + y - xy) + h(xy), \] where \(f\), \(g\), \(h\) are unknown real-valued functions of a real variable. We prove that \(f\), \(g\), \(h\) are affine functions and, moreover, we prove that these equation is stable in the Hyers-Ulam sense.

MSC:
39B82 Stability, separation, extension, and related topics for functional equations
39B62 Functional inequalities, including subadditivity, convexity, etc.
26A51 Convexity of real functions in one variable, generalizations
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