• Prasanna K Sahoo

Articles written in Proceedings – Mathematical Sciences

• Superstability of the generalized orthogonality equation on restricted domains

Chmielinski 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 Chmielinski by proving a theorem: LetDn be a suitable subset of ℝn. If a function f:Dn → ℝn satisfies the inequality ∥〈f(x), f(y)〉¦ ¦〈x,y〉∥ ≤ φ(x,y) for an appropriate control function φ(x, y) and for allx, y ∈ Dn, thenf satisfies the generalized orthogonality equation for anyx, y ∈ Dn.

• On the Stability of Jensen's Functional Equation on Groups

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.

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 5
November 2019

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019