Mathematics – Functional Analysis
Scientific paper
2005-03-05
Proc. Indian Acad. Sci. (Math. Sci.), Vol. 114, No. 3, August 2004, pp. 253-267
Mathematics
Functional Analysis
15 pages
Scientific paper
Chmieli\'{n}ski has proved in the paper [4] the superstability of the generalized orthogonality equation $|< f(x), f(y) >| = |< x, y >|$. In this paper, we will extend the result of Chmieli\'{n}ski by proving a theorem: Let $D_{n}$ be a suitable subset of $ \R^n$. If a function $f\hbox{:} D_{n} \to \R^n$ satisfies the inequality $||< f(x), f(y) >| - |< x, y >|| \leq \phi(x,y)$ for an appropriate control function $\phi(x,y)$ and for all $x, y \in D_{n}$, then $f$ satisfies the generalized orthogonality equation for any $x, y \in D_{n}$.
Jung Soon-Mo
Sahoo Prasanna K.
No associations
LandOfFree
Superstability of the generalized orthogonality equation on restricted domains does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Superstability of the generalized orthogonality equation on restricted domains, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Superstability of the generalized orthogonality equation on restricted domains will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-257127