* Correspondence: [email protected]. kr National Institute for Mathematical Sciences, KT Daeduk 2 Research Center, 463-1 Jeonmin-dong, Yuseong-gu, Daejeon 305-811, Korea Full list of author information is available at the end of the article Abstract Lex X be a normed space and Y be a Banach fuzzy space. Let D = {(x, y) Î X × X : || x|| + ||y|| ≥ d} where d > 0. We prove that the Pexiderized Jensen...

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 ...

We study the Hyers-Ulam stability theory of a four-variate Jensen-type functional equation by considering the approximate remainder φ and obtain the corresponding error formulas. We bring to light the close relation between the β-homogeneity of the norm on F *-spaces and the approximate remainder φ, where we allow p, q, r , and s to be different in their Hyers-Ulam-Rassias stability.