arXiv subjects
Publications and source records attributed to Prasanna K Sahoo.
In this paper we establish the stability of Jensen's functional equation on some classes of groups. We prove that Jensen equation is stable on noncommutative groups such as metabelian groups and $T(2, K)$, where $K$ is an arbitrary commutative field with characteristic different from two. We also prove that any group $A$ can be embedded into some group $G$ such that the Jensen functional equation is stable on $G$.
Chmieliński 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 Chmieliński 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 $||< f(x), f(y) >| - |< x, y >|| \leq ϕ(x,y)$ for an appropriate control function $ϕ(x,y)$ and for all $x, y \in D_{n}$, then $f$ satisfies the generalized orthogonality equation for any $x, y \in D_{n}$.