Jeongwook Chang

THE STABILITY OF THE SINE AND COSINE FUNCTIONAL EQUATIONS IN SCHWARTZ DISTRIBUTIONS

We prove the Hyers-Ulam stability of the sine and cosine functional equations in the spaces of generalized functions such as Schwar- tz distributions, Fourier hyperfunctions, and Gelfand generalized func- tions.

CRITICAL POINT METRICS OF THE TOTAL SCALAR CURVATURE

In this paper, we deal with a critical point metric of the total scalar curvature on a compact manifold M. We prove that if the criti- cal point metric has parallel Ricci tensor, then the manifold is isometric to a standard sphere. Moreover, we show that if an n-dimensional Rie- mannian manifold is a warped product, or has harmonic curvature with non-parallel Ricci tensor, then it cannot be a critical point metric.

HYERS-ULAM STABILITY OF TRIGONOMETRIC FUNCTIONAL EQUATIONS

In this article we prove the Hyers–Ulam stability of trigonometric functional equations.

Stability of Trigonometric Functional Equations in Generalized Functions

We consider the Hyers-Ulam stability of a class of trigonometric functional equations in the spaces of generalized functions such as Schwartz distributions, Fourier hyperfunctions, and Gelfand generalized functions.

CRITICAL POINTS AND WARPED PRODUCT METRICS

It has been conjectured that, on a compact orient able manifold M, a critical point of the total scalar curvature functional restricted the space of unit volume metrics of constant scalar curvature is Einstein. In this paper we show that if a manifold is a 3-dimensional warped product, then (M, g) cannot be a critical point unless it is isometric to the standard sphere.

On the Stability of Trigonometric Functional Equations in Distributions and Hyperfunctions

We consider the Hyers-Ulam stability for a class of trigonometric functional equations in the spaces of generalized functions such as Schwartz distributions and Gelfand hyperfunctions.

On a Generalized Hyers-Ulam Stability of Trigonometric Functional Equations

Let G be an Abelian group, let ℂ be the field of complex numbers, and let f,g:G→ℂ. We consider the generalized Hyers-Ulam stability for a class of trigonometric functional inequalities, |f(x-y)-f(x)g(y)

HARNACK-TYPE INEQUALITIES FOR THE POROUS MEDIUM EQUATION ON A MANIFOLD WITH NON-NEGATIVE RICCI CURVATURE

We derive Harnack-type inequalities for non-negative solutions of the porous medium equation on a complete Riemannian manifold with non-negative Ricci curvature. Along with gradient estimates, reparametrization of a geodesic and time rescaling of a solution are key tools to get the results.

THE CRITICAL POINT EQUATION ON A FOUR DIMENSIONAL WARPED PRODUCT MANIFOLD

On a compact oriented n-dimensional manifold (M n ; g), it has been conjectured that a metric g satisfying the critical point equation (2) should be Einstein. In this paper, we prove that if a manifold (M 4 ;g) is a 4-dimensional oriented compact warped product, then g can not be a solution of CPE with a non-zero solution function f.

On a Weak Version of Hyers–Ulam Stability Theorem in Restricted Domains

In this chapter we consider a weak version of the Hyers–Ulam stability problem for the Pexider equation, Cauchy equation satisfied in restricted domains in a group when the target space of the functions is a 2-divisible commutative group. As the main result we find an approximate sequence for the unknown function satisfying the Pexider functional inequality, the limit of which is the approximate function in the Hyers–Ulam stability theorem.