Stability of Generalized Jensen Equation on Restricted Domains

Details Stability of Generalized Jensen Equation on Restricted Domains Stability of Generalized Jensen Equation on Restricted Domains

2005-11-12

arxiv.org/abs/math/0511320v1

Mathematics

Functional Analysis

14 pages

Scientific paper

In this paper, we establish the conditional Hyers-Ulam-Rassias stability of the generalized Jensen functional equation $r f \left (\frac{sx+ty}{r}) = s g(x) + t h(y)$ on various restricted domains such as inside balls, outside balls, and punctured spaces. In addition, we prove the orthogonal stability of this equation and study orthogonally generalized Jensen mappings on Balls in inner product spaces.

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