• Journal of applied mathematics & informatics
• /
• v.27 no.5_6
• /
• pp.1145-1156
• /
• 2009

In this paper, we consider the existence, uniqueness of the solutions and controllability for the neutral functional integro-differential equations with delay terms by Sadovskii's fixed point theorem.

• Journal of applied mathematics & informatics
• /
• v.38 no.5_6
• /
• pp.469-481
• /
• 2020

In this paper, we consider a control system for semilinear differential equations in Hilbert spaces with Lipschitz continuous nonlinear term. Our method is to find the equivalence of approximate controllability for the given semilinear system and the linear system excluded the nonlinear term, which is based on results on regularity for the mild solution and estimates of the fundamental solution.

• Korean Journal of Mathematics
• /
• v.24 no.2
• /
• pp.297-305
• /
• 2016

In this paper, by using fixed point theorem, we obtain the stability of the following functional equations $$f(pr,qs)+g(ps,qr)={\theta}(p,q,r,s)f(p,q)h(r,s)\\f(pr,qs)+g(ps,qr)={\theta}(p,q,r,s)g(p,q)h(r,s)$$, where G is a commutative semigroup, ${\theta}:G^4{\rightarrow}{\mathbb{R}}_k$ a function and f, g, h are functionals on $G^2$.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.5
• /
• pp.1469-1484
• /
• 2014

In this paper we are concerned with a class of stochastic partial functional differential equations with infinite delay. Supposing that the linear part is a Hille-Yosida operator but not necessarily densely defined and employing the integrated semigroup and random dynamics theory, we present some appropriate conditions to guarantee the existence of a random attractor.

• East Asian mathematical journal
• /
• v.14 no.1
• /
• pp.77-98
• /
• 1998

The purpose of this paper is to introduce and study the semigroups of nonlinear contractions in probabilistic normed spaces and to establish the Crandall-Liggett's exponential formula for some kind of accretive mappings in probabilistic normed spaces. As applications, we utilize these results to study the Cauchy problem for a kind of differential inclusions with accertive mappings in probabilistic normed spaces.

• Bulletin of the Korean Mathematical Society
• /
• v.37 no.2
• /
• pp.401-409
• /
• 2000

In this paper, we determine the structure of ${\kappa}-potent$ elements and regular elements of the semigroup ${\Omega}_n$of doubly stochastic matrices of order n. In connection with this, we find the structure of the matrices X satisfying the equation AXA = A. From these, we determine a condition of a doubly stochastic matrix A whose Moore-Penrose generalized is also a doubly stochastic matrix.

• Journal of the Korean Mathematical Society
• /
• v.57 no.1
• /
• pp.61-88
• /
• 2020

In this paper, we investigate the existence of mild solutions for a class of fractional impulsive evolution equation with periodic boundary condition by means of the method of upper and lower solutions and monotone iterative method. Using the theory of Kuratowski measure of noncompactness, a series of results about mild solutions are obtained. Finally, two examples are given to illustrate our results.

• Journal of applied mathematics & informatics
• /
• v.18 no.1_2
• /
• pp.351-360
• /
• 2005

Let T be a regular semigroup and let S be a regular subsemigroup of T. In this paper we study the relationship between the idempotent separating congruence on S and the idempotent separating congruence on T, when T and S are connected by a splitmap ${\theta} : T {\to} S$.

• Journal of applied mathematics & informatics
• /
• v.16 no.1_2
• /
• pp.559-569
• /
• 2004

In this paper we shall discuss the quasi-perfect automata associated with power automata. We shall give the fact that its power automaton is invertible if an automaton A is quasi-perfect. Moreover, some subgroups and normal subgroups of the characteristic semigroup X(M) will have the very interesting parts in their structures.

• Proceedings of the Korea Contents Association Conference
• /
• 2013.05a
• /
• pp.369-370
• /
• 2013

Orthomodular lattice is a mathematical description of quantum theory which is based on the family CS(H) of all closed subspaces of a Hilbert space H. A partial multiplier is a function F from a non-empty subset D of a commutative semigroup A into A such that F(x)y = xF(y) for every elements x, y in A. In this paper, we define the notion of multipliers on orthomodular lattices and give some properties of multipliers. Also, we characterize some properties of orthomodular lattices by multipliers.