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http://dx.doi.org/10.4134/BKMS.b180607

STABILITY OF PEXIDERIZED JENSEN AND JENSEN TYPE FUNCTIONAL EQUATIONS ON RESTRICTED DOMAINS  

Choi, Chang-Kwon (Department of Mathematics and Liberal Education Institute Kunsan National University)
Publication Information
Bulletin of the Korean Mathematical Society / v.56, no.3, 2019 , pp. 801-813 More about this Journal
Abstract
In this paper, using the Baire category theorem we investigate the Hyers-Ulam stability problem of pexiderized Jensen functional equation $$2f(\frac{x+y}{2})-g(x)-h(y)=0$$ and pexiderized Jensen type functional equations $$f(x+y)+g(x-y)-2h(x)=0,\\f(x+y)-g(x-y)-2h(y)=0$$ on a set of Lebesgue measure zero. As a consequence, we obtain asymptotic behaviors of the functional equations.
Keywords
Baire category theorem; first caetgory; second category; Hyers-Ulam stability; pexiderized Jensen functional equation; pexiderized Jensen type functional equation; restricted domain;
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