The stability of d'Alembert and Jensen type functional equations
نویسندگان
چکیده
منابع مشابه
Non-Archimedean stability of Cauchy-Jensen Type functional equation
In this paper we investigate the generalized Hyers-Ulamstability of the following Cauchy-Jensen type functional equation$$QBig(frac{x+y}{2}+zBig)+QBig(frac{x+z}{2}+yBig)+QBig(frac{z+y}{2}+xBig)=2[Q(x)+Q(y)+Q(z)]$$ in non-Archimedean spaces
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In 1941 D.H. Hyers solved the well-known Ulam stability problem for linear mappings. In 1951 D.G. Bourgin was the second author to treat the Ulam problem for additive mappings. In 1982–2005 we established the Hyers–Ulam stability for the Ulam problem of linear and nonlinear mappings. In 1998 S.-M. Jung and in 2002–2005 the authors of this paper investigated the Hyers–Ulam stability of additive ...
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متن کاملOn the stability of generalized d'Alembert and Jensen functional equations
where f , g are two unknown functions to be determined. Equation (A f g), raised by Wilson, is called the Wilson equation sometimes, and (Ag f ) is raised by Kannappan and Kim [9]. Let g(x) ≡ k in (Ag f ). Then we have f (x + y) + f (x − y) = 2k f (y) for all x, y ∈ G. Putting y = 0 in this equation we have f (x)= k f (0). Hence f is a constant function. Let g(y)≡ 1 in (A f g). Then we have the...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2007
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2006.01.062