• Bulletin of the Korean Mathematical Society
• /
• v.47 no.5
• /
• pp.987-996
• /
• 2010

In this paper, we investigate the Cauchy-Rassias stability in Banach spaces and also the Cauchy-Rassias stability using the alternative fixed point for the functional equation: $$f(\frac{sx+ty}{2}+rz)+f(\frac{sx+ty}{2}-rz)+f(\frac{sx-ty}{2}+rz)+f(\frac{sx-ty}{2}-rz)=s^2f(x)+t^2f(y)+4r^2f(z)$$ for any fixed nonzero integers s, t, r with $r\;{\neq}\;{\pm}1$.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 1995.10b
• /
• pp.326-330
• /
• 1995

We define a PL-limit structure and a PL-Cauchy structure and obtain a completion of a separated PL-Cauchy structure.

• Journal of KIISE:Software and Applications
• /
• v.37 no.8
• /
• pp.591-598
• /
• 2010

In this study, we propose a new method for generating candidate solutions based on the Cauchy probability distribution in order to complement the shortcoming of the solutions generated by the normal distribution. The Cauchy probability distribution has infinite mean and variance, and it has rather large probability in the tail region relative to the normal distribution. Thus, the Cauchy distribution can yield higher probabilities of generating candidate solutions of large-varied variables, which in turn has an advantage of searching wider area of variable space. In order to compare and analyze the performance of the proposed method against the conventional method, we carried out an experiment using benchmarking problems of real valued function. From the result of the experiment, we found that the proposed method based on the Cauchy distribution outperformed the conventional one for all benchmarking problems, and verified its superiority by the statistical hypothesis test.

• Korean Journal of Mathematics
• /
• v.22 no.1
• /
• pp.139-150
• /
• 2014

We introduce the concept of generalized (${\theta}$, ${\phi}$)-derivations on Banach algebras, and prove the Cauchy-Rassias stability of generalized (${\theta}$, ${\phi}$)-derivations on Banach algebras.

• Journal of the Chungcheong Mathematical Society
• /
• v.19 no.1
• /
• pp.27-36
• /
• 2006

In [1], the concept of generalized (${\theta}$, ${\phi}$)-derivations on rings was introduced. We introduce the concept of linear ${\theta}$-derivations on $JB^*$-triples, and prove the Cauchy-Rassias stability of linear ${\theta}$-derivations on $JB^*$-triples.

• Journal of applied mathematics & informatics
• /
• v.8 no.2
• /
• pp.581-590
• /
• 2001

In this paper we prove a local stability of Gavruta’s theorem for the generalized Hyers-Ulam-Rassias Stability of Cauchy functional equation.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.2
• /
• pp.441-444
• /
• 2013

It is shown that any two-dimensional globally hyperbolic spacetime with noncompact Cauchy surfaces has no null cut points.

• Bulletin of the Korean Mathematical Society
• /
• v.37 no.2
• /
• pp.303-316
• /
• 2000

The Cauchy problem for degenerate parabolic equations with absorption is studied. We prove the existence of a fundamental solution. Also a Harnack type inequality is established and the existence and uniqueness of initial trace for nonnegative solutions is shown.

• Korean Journal of Mathematics
• /
• v.5 no.1
• /
• pp.1-8
• /
• 1997

In this note, we study on fuzzy uniform convergences of sequences of fuzzy numbers, and sequences of fuzzy functions.

• Korean Journal of Mathematics
• /
• v.22 no.4
• /
• pp.659-670
• /
• 2014

In this paper, we prove the Hyers-Ulam stability of homomorphisms in fuzzy Banach algebras and of derivations on fuzzy Banach algebras associated to the Cauchy-Jensen functional equation.