On Stability of the Equation of Homogeneous Functions on Topological Spaces

Stefan Czerwik ()
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Stefan Czerwik: Silesian University of Technology

Chapter Chapter 7 in Functional Equations in Mathematical Analysis, 2011, pp 87-96 from Springer

Abstract: Abstract Let K be a cone of a linear space X and Y a sequentially complete locally convex linear topological Hausdorff space. Let f : K → Y and g: K→ Y satisfy $${\alpha }^{-1}f(\alpha x) - g(x) \in U,\quad \alpha \in A,\ x \in K,$$ where U is a bounded subset of Y and A ⊂ [1, ∞). Under some additional assumptions we prove that there exists exactly one positively homogeneous function F : K → Y such that the differences F − f and F ;− g are bounded on K, i.e. the equation of homogeneous functions is stable in the Ulam–Hyers sense.

Keywords: Functional equations; Stability; Homogeneous functions (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4614-0055-4_7

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DOI: 10.1007/978-1-4614-0055-4_7

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