Title of article :
Asymptotic behavior of generalized quadratic mappings
Author/Authors :
Kim, Hark-Mahn Department of Mathematics - Chungnam National University, Daejeon, Korea , Chang, Ick-Soon Department of Mathematics - Chungnam National University, Daejeon, Korea
Abstract :
We show in this paper that a mapping f satisfies
the following functional equation
⨄x2,⋯,xd+1df(x1)=2d∑i=1d+1f(xi),
if and only if it is quadratic. In addition, we investigate generalized Hyers-Ulam stability problem for the equation, and thus obtain an asymptotic property of quadratic mappings as applications.
Keywords :
Stability , Parallel polyhedron equality , Generalized quadratic mappings
Journal title :
International Journal of Nonlinear Analysis and Applications
