• Honam Mathematical Journal
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• v.39 no.4
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• pp.575-590
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• 2017

A new class of functions called $R_{\theta}$-supercontinuous functions is introduced. Their basic properties are studied and their place in the hierarchy of strong variants of continuity, which already exist in the literature, is elaborated. The class of $R_{\theta}$-supercontinuous functions properly contains the class of $R_z$-supercontinuous functions [39] which in turn properly contains the class of $R_{cl}$-supercontinuous functions [43] and so includes all cl-supercontinuous (clopen continuous) functions ([38], [34]) and is properly contained in the class of $R_{\delta}$-supercontinuous functions [24].

• Communications of the Korean Mathematical Society
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• v.26 no.1
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• pp.115-124
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• 2011

In this paper, some fuzzy fixed point theorems for fuzzy mappings are established by considering the nonempty closed $\alpha$-cut sets. Some importance observations are also discussed. Our results clearly extend, generalize and improve the corresponding results in the literatures, which have given most of their attention to the class of fuzzy sets with nonempty compact or closed and bounded $\alpha$-cut sets.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.37-51
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• 2002

Let X be a reflexive Banach space with a uniformly Gateaux differentiable norm, C a nonempty bounded open subset of X, and T a continuous mapping from the closure of C into X which is locally pseudo-contractive mapping on C. We show that if the closed unit ball of X has the fixed point property for nonexpansive self-mappings and T satisfies the following condition: there exists z $\in$ C such that ∥z-T(z)∥<∥x-T(x)∥ for all x on the boundary of C, then the trajectory tlongrightarrowz$_{t}$$\in$C, t$\in$[0, 1) defined by the equation z$_{t}$ = tT(z$_{t}$)+(1-t)z is continuous and strongly converges to a fixed point of T as t longrightarrow 1￣.ow 1￣.

• Kyungpook Mathematical Journal
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• v.51 no.2
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• pp.205-215
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• 2011

Given a knot diagram D, we construct a semi-threading circle of it which can be an axis of D as a closed braid depending on knot diagrams. In particular, we consider semi-threading circles of minimal diagrams of a knot with respect to overpasses which give us some information related to the braid index. By this notion, we try to give another proof of the fact that, for every nontrivial knot K, the braid index b(K) of K is not less than the minimum number l(K) of overpasses of diagrams. Also, they are the same for a torus knot.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.13-30
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• 2010

Let C be a nonempty closed convex subset of a real Hilbert space H. Consider the following iterative algorithm given by $x_0\;{\in}\;C$ arbitrarily chosen, $x_{n+1}\;=\;{\alpha}_n{\gamma}f(W_nx_n)+{\beta}_nx_n+((1-{\beta}_n)I-{\alpha}_nA)W_nP_C(I-s_nB)x_n$, ${\forall}_n\;{\geq}\;0$, where $\gamma$ > 0, B : C $\rightarrow$ H is a $\beta$-inverse-strongly monotone mapping, f is a contraction of H into itself with a coefficient $\alpha$ (0 < $\alpha$ < 1), $P_C$ is a projection of H onto C, A is a strongly positive linear bounded operator on H and $W_n$ is the W-mapping generated by a finite family of nonexpansive mappings $T_1$, $T_2$, ${\ldots}$, $T_N$ and {$\lambda_{n,1}$}, {$\lambda_{n,2}$}, ${\ldots}$, {$\lambda_{n,N}$}. Nonexpansivity of each $T_i$ ensures the nonexpansivity of $W_n$. We prove that the sequence {$x_n$} generated by the above iterative algorithm converges strongly to a common fixed point $q\;{\in}\;F$ := $\bigcap^N_{i=1}F(T_i)\;\bigcap\;VI(C,\;B)$ which solves the variational inequality $\langle({\gamma}f\;-\;A)q,\;p\;-\;q{\rangle}\;{\leq}\;0$ for all $p\;{\in}\;F$. Using this result, we consider the problem of finding a common fixed point of a finite family of nonexpansive mappings and a strictly pseudocontractive mapping and the problem of finding a common element of the set of common fixed points of a finite family of nonexpansive mappings and the set of zeros of an inverse-strongly monotone mapping. The results obtained in this paper extend and improve the several recent results in this area.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.1
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• pp.139-143
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• 2015

In this paper, we prove that (r, s)-semi-irresolute image of the (r, s)-semi-${\theta}$-connected set is also (r, s)-semi-${\theta}$-connected. Moreover, we prove that an (r, s)-semi-irresolute mapping preserves (r; s)-$S^*$-closedness.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.667-680
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• 2014

In this paper, $\mathcal{I}$-scattered spaces are introduced, and their characterizations and properties are given. We prove that (X, ${\tau}$) is scattered if and only if (X, ${\tau}$, $\mathcal{I}$) is $\mathcal{I}$-scattered for any ideal $\mathcal{I}$ on X.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.13-22
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• 2016

We introduce the concepts of double (r, s)(u, v)-preopen sets, double (r, s)(u, v)-preclosed sets and double pairwise (r, s)(u, v)-precontinuous mappings in double bitopological spaces and investigate some of their characteristic properties.

• Korean Journal of Mathematics
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• v.12 no.1
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• pp.33-40
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• 2004

Let $E,F{\subset}(R^*)^n$ be non-empty sets and let ${\Gamma}$ be this family of all closed curves which join E to F in $(R^*)^n$. In this paper, we shall study the problems of finding properties for the conductance $C({\Gamma})$. And we obtain the inequalities in connection with capacity of condensers.

• East Asian mathematical journal
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• v.15 no.2
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• pp.325-336
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• 1999

In this paper, we prove that any $\lambda$-firmly nonexpansive mapping ($0<\lambda<1)T:C{\rightarrow}C$ has a fixed point in C whenever C is a finite union of nonempty, bounded, closed and convex subsets of a metric space of hyperbolic type.