Byungbae Kim

Bessel's Differential Equation and Its Hyers-Ulam Stability

We solve the inhomogeneous Bessel differential equation and apply this result to obtain a partial solution to the Hyers-Ulam stability problem for the Bessel differential equation.

LOCAL STABILITY OF THE ADDITIVE FUNCTIONAL EQUATION AND ITS APPLICATIONS

The main purpose of this paper is to prove the Hyers-Ulam stability of the additive functional equation for a large class of unbounded domains. Furthermore, by using the theorem, we prove the stability of Jensen’s functional equation for a large class of restricted domains.

On the stability of the quadratic functional equation on bounded domains

A result of Skof and Terracini will be generalized; More precisely, we will prove that if a functionf : [-t, t]n →E satisfies the inequality (1) for some δ > 0 and for allx, y ∈ [-t, t]n withx + y, x - y ∈ [-t, t]n, then there exists a quadratic functionq: ℝn →E such that ∥f(x) -q(x)∥ < (2912n2 + 1872n + 334)δ for anyx ∈ [-t, t]n.

Unit-circle-preserving mappings

We prove that if a one-to-one mapping f:ℝn→ℝn(n≥2) preserves the unit circles, then f is a linear isometry up to translation.

Simple Harmonic Oscillator Equation and Its Hyers-Ulam Stability

We solve the inhomogeneous simple harmonic oscillator equation and apply this result to obtain a partial solution to the Hyers-Ulam stability problem for the simple harmonic oscillator equation.

MAPPINGS WHICH PRESERVE REGULAR DODECAHEDRONS

We prove that if a one-to-one mapping f : ℝ 3 → ℝ 3 preserves regular dodecahedrons, then f is a linear isometry up to translation.

MAPPINGS PRESERVING REGULAR HEXAHEDRONS

We will prove that if a one-to-one mapping f:ℝ3→ℝ3 preserves regular hexahedrons, then f is a linear isometry up to translation.