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On Stability of the Equation of Homogeneous Functions on Topological Spaces

In: Functional Equations in Mathematical Analysis

Author

Listed:
  • Stefan Czerwik

    (Silesian University of Technology)

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.

Suggested Citation

  • Stefan Czerwik, 2011. "On Stability of the Equation of Homogeneous Functions on Topological Spaces," Springer Optimization and Its Applications, in: Themistocles M. Rassias & Janusz Brzdek (ed.), Functional Equations in Mathematical Analysis, chapter 0, pages 87-96, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-0055-4_7
    DOI: 10.1007/978-1-4614-0055-4_7
    as

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