• Soon-Mo Jung

Articles written in Proceedings – Mathematical Sciences

• Some functional equations originating from number theory

We will introduce new functional equations (3) and (4) which are strongly related to well-known formulae (1) and (2) of number theory, and investigate the solutions of the equations. Moreover, we will also study some stability problems of those equations.

• On some congruence with application to exponential sums

We will study the solution of a congruence,xg1/2)ωg(2n) mod 2n, depending on the integersg andn, where ωg(2n) denotes the order ofg modulo 2n. Moreover, we introduce an application of the above result to the study of an estimation of exponential sums.

• 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.

• # Proceedings – Mathematical Sciences

Volume 130, 2020
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019