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

• Journal of the Chungcheong Mathematical Society
• /
• v.36 no.4
• /
• pp.279-288
• /
• 2023

We obtain a Chandrabhan type fixed point theorem for a multimap having a non-compact domain and a weakly closed graph, and taking convex values only on a quasi-convex subset of Hausdorff locally convex topological vector space. We introduce the definition of Chandrabhan-set and find a sufficient condition for every countably condensing multimap to have a relatively compact Chandrabhan-set. Finally, we establish a new version of Sadovskii fixed point theorem for multimaps.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.6 no.1
• /
• pp.70-76
• /
• 2006

Some Stampacchia type of generalized weak vector quasivariational-like inequalities for fuzzy mappings was introduced and the existence of solutions to them under non-compact assumption was considered using the particular form of the generalized Ky Fan's section theorem due to Park [15]. As a corollary, Stampacchia type of generalized vector quasivariational-like inequalities for fuzzy mappings was studied under compact assumption using Ky Fan's section theorem [7].

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

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

• The Pure and Applied Mathematics
• /
• v.25 no.1
• /
• pp.1-5
• /
• 2018

It is proved that 'maximum' is actually attained in the following risk measure representation $${\rho}_m(X)={max \atop Q{\in}Q_m}E_Q[-X]$$.

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

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.3
• /
• pp.455-465
• /
• 2010

In this paper, by using the semi-order method, two new existence theorems of coupled quasi-solutions for a class of nonlinear operator equations in Banach spaces are proved under some suitable conditions.

• Communications of the Korean Mathematical Society
• /
• v.18 no.1
• /
• pp.59-63
• /
• 2003

Let A be a $C^*$-algebra and $K_{A}$ its Pedersen's ideal. A is called a PCS-algebra if the multiplier $\Gamma(K_{A})\;of\;K_{A}$ is the multiplier M(A) of A. J. Mack [5]characterized PCS-algebras by weak compactness on the spectrum of A. We give a new simple proof of this Mack's result using the concept of semicontinuity and N. C. Phillips' description of $\Gamma(K_{A})$.

• Journal of the Korean Mathematical Society
• /
• v.48 no.3
• /
• pp.641-653
• /
• 2011

The intermediate value theorem for a continuous real valued function is a kind of Bolzano's theorem. Similar results also hold for compact, monotone or accretive mappings in Banach spaces. In this paper we give multivalued versions of Bolzano's theorem.

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