• Korean Journal of Mathematics
• /
• v.23 no.3
• /
• pp.357-370
• /
• 2015

In this paper, we introduce the concept of (m, n)-ideals in a non-associative ordered structure, which is called an ordered Abel-Grassmann's groupoid, by generalizing the concept of (m, n)-ideals in an ordered semigroup [14]. We also study the (m, n)-regular class of an ordered AG-groupoid in terms of (m, n)-ideals.

• Communications of the Korean Mathematical Society
• /
• v.11 no.2
• /
• pp.315-321
• /
• 1996

Recently, N. Kehayopulu [4] introduced the concepts of weakly prime ideals of ordered semigroups. In this paper, we define the concepts of left(right) weakly prime and left(right) semiregular. Also we investigate the properties of them.

• Journal of the Korean Mathematical Society
• /
• v.39 no.5
• /
• pp.775-782
• /
• 2002

In this paper we prove the existence of mild soultions for semilinear differential equations in a Banach space. The results are obtained by using the semigroup theory and the Schaefer fixed point theorem. An example is provided to illustrate the theory.

• Journal of the Korean Mathematical Society
• /
• v.41 no.4
• /
• pp.647-665
• /
• 2004

The existence of solutions for the nonlinear functional differential equation with nonlocal conditions governed by the variational inequality is studied. The regularity and a variation of solutions of the equation are also given.

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.4
• /
• pp.691-700
• /
• 2009

We prove the local existence of classical solutions of quasi-linear integrodifferential equations in Banach spaces. The results are obtained by using fractional powers of operators and the Schauder fixed-point theorem. An example is provided to illustrate the theory.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.1
• /
• pp.13-27
• /
• 2014

The purpose of this paper is to derive a perturbation theory of evolution systems of the hyperbolic second order hyperbolic equations. We give an example of a partial functional equation as an application of the preceding result in case of the mixed problems for hyperbolic equations of second order with unbounded principal operators.

• Bulletin of the Korean Mathematical Society
• /
• v.39 no.4
• /
• pp.527-534
• /
• 2002

The weighted shifts have been made a central role in the study of κ-hyponormality for hyponormal and subnormal operators in discrete notion. In this note we discuss the κ-hyponormality of weighted translation semigroups with a symbol function in continuous notion.

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.2
• /
• pp.295-301
• /
• 2009

We prove the Hyers-Ulam stability of a Pexiderized exponential equation of mappings f, g, h : $G{\times}S{\rightarrow}{\mathbb{C}}$, where G is an abelian group and S is a commutative semigroup which is divisible by 2. As an application we obtain a stability theorem for Pexiderized exponential equation in Schwartz distributions.

• Communications of the Korean Mathematical Society
• /
• v.32 no.3
• /
• pp.579-600
• /
• 2017

In this paper we consider a semilinear pseudoparabolic equation with polynomial nonlinearity and infinite delay. We first prove the existence and uniqueness of weak solutions by using the Galerkin method. Then, we prove the existence of a compact global attractor for the continuous semigroup associated to the equation. The existence and exponential stability of weak stationary solutions are also investigated.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.1
• /
• pp.319-330
• /
• 2018

This paper is concerned with the global asymptotic stability of strong solutions for a class of semilinear evolution equations with nonlocal initial conditions on infinite interval. The discussion is based on analytic semigroups theory and the gradually regularization method. The results obtained in this paper improve and extend some related conclusions on this topic.