• The Pure and Applied Mathematics
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• v.4 no.2
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• pp.115-119
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• 1997

We show that if $f_{i}$:$X_{i}$ longrightarrow Y is strongly continuous(resp. weakly continuous, set connected, compact, feebly continuous, almost-continuous, strongly $\theta$-continuous, $\theta$-continuous, g-continuous, V-map), then F : $X_1 \bigoplus X_2$longrightarrow Y is strongly continuous(resp.weakly continuous, set connected, compact, feebly continuous, almost-continuous, strongly $\theta$-continuous, $\theta$-continuous, g-continuous, V-map).

• Korean Journal of Mathematics
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• v.17 no.2
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• pp.219-231
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• 2009

We show the existence of at least four solutions for the perturbed parabolic equation with Dirichlet boundary condition and periodic condition when the nonlinear part cross two eigenvalues of the eigenvalue problem of the Laplace operator with boundary condition. We obtain this result by using the Leray-Schauder degree theory, the finite dimensional reduction method and the geometry of the mapping. The main point is that we restrict ourselves to the real Hilbert space instead of the complex space.

• Journal of the Chungcheong Mathematical Society
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• v.3 no.1
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• pp.103-110
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• 1990

Let K be a nonempty weakly compact convex subset of a Banach space X and T : K ${\rightarrow}$ C(X) a nonexpansive mapping satisfying $P_T(x){\cap}clI_K(x){\neq}{\emptyset}$. We first show that if I - T is semiconvex type then T has a fixed point. Also we obtain the same result without the condition that I - T is semiconvex type in a Banach space satisfying Opial's condition. Lastly we extend the result of [5] to the case, that T is an 1-set contraction mapping.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.4
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• pp.281-284
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• 2009

In [8], we introduced the concept of fuzzy r-minimal structure which is an extension of smooth fuzzy topological spaces and fuzzy topological spaces in Chang's sense. And we also introduced and studied the fuzzy r-M continuity. In this paper, we introduce the concepts of fuzzy r-minimal compactness on fuzzy r-minimal compactness and nearly fuzzy r-minimal compactness, almost fuzzy r-minimal spaces and investigate the relationships between fuzzy r-M continuous mappings and such types of fuzzy r-minimal compactness.

• Honam Mathematical Journal
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• v.27 no.2
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• pp.251-265
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• 2005

In this paper, we introduce a generalized vector quasivariational like inequality for fuzzy mappings and show the existence of solutions under compact assumption.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.1 no.1
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• pp.50-55
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• 2001

We generalize mainly the concept of c-continuity of a mapping due to Gentry and Hoyle III in fuzzy setting. And we investigate some properties of fuzzy c-continuous mappings.

• Honam Mathematical Journal
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• v.27 no.3
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• pp.445-463
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• 2005

In this paper, we introduce a Stampacchia type of generalized weak vector quasivariational-like inequalities for fuzzy mappings and consider the existence of solutions to them under non-compact assumption.

• Korean Journal of Mathematics
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• v.27 no.3
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• pp.819-830
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• 2019

This paper is mainly concerned with the existence and uniqueness of fixed points of $f:X^k{\rightarrow}X$, $k{\in}{\mathbb{N}}$, where X is a quasi-partial metric space and mapping f satisfies appropriate conditions. Results are also supported with relevant examples.

• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.761-790
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• 2021

For given spaces X and Y, let map(X, Y) and map_*(X, Y) be the unbased and based mapping spaces from X to Y, equipped with compact-open topology respectively. Then let map(X, Y ; f) and map_*(X, Y ; g) be the path component of map(X, Y) containing f and map_*(X, Y) containing g, respectively. In this paper, we compute cohomotopy groups of suspended complex plane π^n+m(ΣⁿℂP²) for m = 6, 7. Using these results, we classify path components of the spaces map(ΣⁿℂP², S^m) up to homotopy equivalence. We also determine the generalized Gottlieb groups G_n(ℂP², S^m). Finally, we compute homotopy groups of mapping spaces map(ΣⁿℂP², S^m; f) for all generators [f] of [ΣⁿℂP², S^m], and Gottlieb groups of mapping components containing constant map map(ΣⁿℂP², S^m; *).

• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.333-342
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• 2007

Suppose that ${\mu}$ is a finite positive Borel measure on the unit ball $B{\subset}C^n$. The boundary of B is the unit sphere $S=\{z:{\mid}z{\mid}=1\}$. Let ${\sigma}$ be the rotation-invariant measure on S such that ${\sigma}(S)=1$. In this paper, we will show that if $sup_{{\zeta}{\in}S}\;{\int}_{B}\;P(z,{\zeta})d{\mu}(z)$<${\infty}$ where $P(z,{\zeta})$ is the Poission-Szeg$\ddot{o}$ kernel for B, then ${\mu}$ is a Carleson measure. We will also show that if $sup_{{\zeta}{\in}S}\;{\int}_{B}\;P(z,{\zeta})d{\mu}(z)$<${\infty}$, then the operator T such that T(f) = P[f] is compact as a mapping from $L^p(\sigma)$ into $L^p(B,d{\mu})$.