Abstract
In 1967, M. Hosszú introduced the functional equation \(f(x+y-xy)=f(x)+f(y)-f(xy)\) in a presentation at a meeting on functional equations held in Zakopane, Poland. In honor of M. Hosszú, this equation is called Hosszú’s functional equation. As one can easily see, Hosszú’s functional equation is a kind of generalized form of the additive Cauchy functional equation. In Section 4.1, it will be proved that Hosszú’s equation is stable in the sense of C. Borelli. We discuss the Hyers–Ulam stability problem of Hosszú’s equation in Section 4.2. In Section 4.3, Hosszú’s functional equation will be generalized, and the stability (in the sense of Borelli) of the generalized equation will be proved. It is surprising that Hosszú’s functional equation is not stable on the unit interval. It will be discussed in Section 4.4. In the final section, we will survey the Hyers–Ulam stability of Hosszú’s functional equation of Pexider type.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Jung, SM. (2011). Hosszú’s Functional Equation. In: Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis. Springer Optimization and Its Applications(), vol 48. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9637-4_4
Download citation
DOI: https://doi.org/10.1007/978-1-4419-9637-4_4
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-9636-7
Online ISBN: 978-1-4419-9637-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)