On a Jensen–Hosszú equation I
Abstract
We solve functional equation of the form
f(x+y−xy) + f(xy) = 2f((x+y)/2)
in the class of functions transforming the space of all reals into itself. We also prove that this equation is stable in the Hyers-Ulam’s sense.
Keywords
general solutions of functional equations; Jensen and Hoszú functional equations; Hyers–Ulam stability
References
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3. Kuczma M., An Introduction to the Theory of Functional Equations and Inequalities. Cauchy’s Equation and Jensen’s Inequality, Silesian University and PWN, Warszawa– Kraków–Katowice, 1985.
4. Whitney H., On functions with bounded n-th differences , J. Math. Pures Appl. (9) 36 (1957), 67–95.
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
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