• 충청수학회지
• /
• 제22권1호
• /
• pp.101-116
• /
• 2009

In 1940 S.M. Ulam proposed the famous Ulam stability problem. In 1941 D.H. Hyers solved the well-known Ulam stability problem for additive mappings subject to the Hyers condition on approximately additive mappings. In this paper we improve results for Jensen type mappings and establish new theorems about the Ulam stability of additive and alternative Jensen type mappings.

• Journal of applied mathematics & informatics
• /
• 제27권5_6호
• /
• pp.1473-1479
• /
• 2009

We introduce the resistant length and examine its properties. We also consider the geometric applications of resistant length to the boundary behavior of analytic functions, conformal mappings and derive the theorem in connection with the fundamental sequences, purely geometric problems. The method of resistant length leads a simple proofs of theorems. So it shows us the usefulness of the method of resistant length.

• Journal of applied mathematics & informatics
• /
• 제18권1_2호
• /
• pp.603-611
• /
• 2005

We present some geometric applications of extremal length. The method of extremal length leads a simple proofs of theorems. And we consider the applications of extremal length to the boundary behavior of analytic functions and derive theorems in connection with the conformal mappings. It shows us the usefulness of the method of extremal length.

• Kyungpook Mathematical Journal
• /
• 제55권1호
• /
• pp.91-101
• /
• 2015

In this paper, we investigate the stability of the functional equation f(-x + y + z + w) + f(x - y + z + w) + f(x + y - z + w) + f(x + y + z - w) = 3f(x) + f(-x) + 3f(y) + f(-y) + 3f(z) + f(-z) + 3f(w) + f(-w) by using the direct method in the sense of Hyers.

• Kyungpook Mathematical Journal
• /
• 제58권2호
• /
• pp.291-305
• /
• 2018

In this paper, we prove a general uniqueness theorem which is useful for proving the uniqueness of the relevant additive mapping, quadratic mapping, cubic mapping, quartic mapping, or the additive-quadratic-cubic-quartic mapping when we investigate the (generalized) Hyers-Ulam stability.

• Korean Journal of Mathematics
• /
• 제14권2호
• /
• pp.281-289
• /
• 2006

We introduce the resistant length and examine its properties. We also consider the geometric applications of resistant length to the boundary behavior of analytic functions, conformal mappings and derive the theorem in connection with the cluster sets, purely geometric problems. The method of resistant length leads a simple proofs of theorems. So it shows us the usefulness of the method of resistant length.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제13권3호
• /
• pp.217-224
• /
• 2009

In this paper we present an approximation method of quadric surface using quartic spline. Our method is based on the approximation of quadratic rational B$\acute{e}$zier patch using quartic B$\acute{e}$zier patch. We show that our approximation method yields $G^1$ (tangent plane) continuous quartic spline surface. We illustrate our results by the approximation of helicoid-like surface.

• Kyungpook Mathematical Journal
• /
• 제60권1호
• /
• pp.133-144
• /
• 2020

We will prove the generalized Hyers-Ulam stability of cubic-quadratic-additive type functional equations and general cubic functional equations whose solutions are cubic-quadratic-additive mappings and general cubic mappings, respectively.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제10권3호
• /
• pp.193-198
• /
• 2003

Let X and Y be n-dimensional Euclidean spaces with $n\;{\geq}\;3$. In this paper, we generalize a classical theorem of Bookman and Quarles by proving that if a mapping, from a half space of X into Y, preserves a distance $\rho$, then the restriction of f to a subset of the half space is an isometry.

• 대한수학회논문집
• /
• 제36권4호
• /
• pp.771-782
• /
• 2021

In this paper we introduce generalized weakly semi-conformally symmetric manifold, a generalization of weakly symmetric manifold. We study some basic properties and obtain the forms of the scalar curvature of such manifold. In the last section an example is given to ensure the existence of such manifold.