• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.547-564
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• 1994

Let X be a real Banach space. We consider the existence of solutions of the abstract nonlinear functional evolution equation : $$ (E) \frac{du(t)}{dt} + A(t)u(t) + F(u)(t) \ni h(t), $$ $$ u(s) = x_o \in D(A(s)), 0 \leq s \leq t \leq T, $$ where u : $[s, T] \to x$ is an unknown function, ${A(t) : 0 \leq t \leq T}$ is a given family of nonlinear (possibly multivalued) operators in X, and $F : C([s, t];X) \to L^{\infty}([s, X];X)$ and $h : [s, T] \to X$ are given functions.

• Bulletin of the Korean Space Science Society
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• 1997.04a
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• pp.33.2-33
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• 1997

No Abstract.See Full-text

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.177-195
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• 2021

In this paper, we introduce the modification of a generalized (Ψ, L)-weak contraction and we prove some coincidence point results for self-mappings G, T and S, and some fixed point results for some maps by using a (c)-comparison function and a comparison function in the sense of a b-metric space.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.65-72
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• 2012

Let T > 0 be given. Let $(C[0,T],m_{\varphi})$ be the analogue of Wiener measure space, associated with the Borel proba-bility measure ${\varphi}$ on ${\mathbb{R}}$, let $(L_{2}[0,T],\tilde{\omega})$ be the centered Gaussian measure space with the correlation operator $(-\frac{d^{2}}{dx^{2}})^{-1}$ and ${\el}_2,\;\tilde{m}$ be the abstract Wiener measure space. Let U be the space of all sequence $<c_{n}>$ in ${\el}_{2}$ such that the limit $lim_{{m}{\rightarrow}\infty}\;\frac{1}{m+1}\;\sum{^{m}}{_{n=0}}\;\sum_{k=0}^{n}\;c_{k}\;cos\;\frac{k{\pi}t}{T}$ converges uniformly on [0,T] and give a set function m such that for any Borel subset G of $\el_2$, $m(\mathcal{U}\cap\;P_{0}^{-1}\;o\;P_{0}(G))\;=\tilde{m}(P_{0}^{-1}\;o\;P_{0}(G))$. The goal of this note is to study the relationship among the measures $m_{\varphi},\;\tilde{\omega},\;\tilde{m}$ and $m$.

• Bulletin of the Korean Mathematical Society
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• v.34 no.3
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• pp.385-394
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• 1997

In this paper, we prove in p-uniforlmy convex space a fixed point theorem for a class of mappings T satsfying: for each x, y in the domain and for n = 1, 2, 3, $\cdots$, $$ \left\$\mid$ T^n x - T^n y \right\$\mid$ \leq a \cdot \left\$\mid$ x - y \right\$\mid$ + b(\left\$\mid$ x - T^n x \right\$\mid$ + \left\$\mid$ y - T^n y \right\$\mid$) + c(\left\$\mid$ c - T^n y \right\$\mid$ + \left\$\mid$ y - T^n x \right\$\mid$, $$ where a, b, c are nonnegative constants satisfying certain conditions. Further we establish some fixed point theorems for these mappings in a Hilbert space, in $L^p$ spaces, in Hardy spaces $H^p$ and in Sobolev spaces $H^{p,k}$ for 1 < p < $\infty$ and k $\leq$ 0. As a consequence of our main result, we also the results of Goebel and Kirk [7], Lim [8], Lifshitz [12], Xu [20] and others.

• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.77-95
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• 2012

For a bounded linear operator T we prove the following assertions: (a) If T is algebraically (p, k)-quasihyponormal, then T is a-isoloid, polaroid, reguloid and a-polaroid. (b) If $T^*$ is algebraically (p, k)-quasihyponormal, then a-Weyl's theorem holds for f(T) for every $f{\in}Hol({\sigma}T))$, where $Hol({\sigma}(T))$ is the space of all functions that analytic in an open neighborhoods of ${\sigma}(T)$ of T. (c) If $T^*$ is algebraically (p, k)-quasihyponormal, then generalized a-Weyl's theorem holds for f(T) for every $f{\in}Hol({\sigma}T))$. (d) If T is a (p, k)-quasihyponormal operator, then the spectral mapping theorem holds for semi-B-essential approximate point spectrum $\sigma_{SBF_+^-}(T)$, and for left Drazin spectrum ${\sigma}_{lD}(T)$ for every $f{\in}Hol({\sigma}T))$.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.309-317
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• 2016

Let V be a Euclidean Jordan algebra with a symmetric cone K. We show that for a Z-transformation L with the additional property L(K) ⊆ K (which we will call ’cone-preserving’), GUS ⇔ strictly copositive on K ⇔ monotone + P. Specializing the result to the Stein transformation S_A(X) := X - AXA^T on the space of real symmetric matrices with the property $S_A(S^n_+){\subseteq}S^n_+$, we deduce that S_A GUS ⇔ I ± A positive definite.

• Korean Journal of Mathematics
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• v.23 no.1
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• pp.47-64
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• 2015

We express generalized Fourier-Feynman transform and convolution product of functionals in a Banach algebra $\mathcal{S}(L^2_{a,b}[0,T])$ as limits of function space integrals on $C_{a,b}[0,T]$. Moreover we obtain change of scale formulas for function space integrals related with generalized Fourier-Feynman transform and convolution product of these functionals.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.775-780
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• 1998

In this paper it is shown that Dunford-Pettis operators obey the "Pettis-divisor property": if T is a Dunford-Pettis operator from $L_1$($\mu$) to a Banach space X, then there is a non-Pettis representable operator S : $L_1$($\mu$)longrightarrow$L_1$($\mu$) such that To S is Pettis representable.

• Journal of The Korean Astronomical Society
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• v.50 no.1
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• pp.7-20
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• 2017

We carry out the study of $850{\mu}m$ sources in a part of the XMM-LSS field. The $850{\mu}m$ imaging data were obtained by the SCUBA-2 on the James Clerk Maxwell Telescope (JCMT) for three days in July 2015 with an integration time of 6.1 hours, covering a circular area with a radius of 15'. We choose the central area up to a radius of 9'.15 for the study, where the noise distribution is relatively uniform. The root mean square (rms) noise at the center is 2.7 mJy. We identify 17 sources with S/N > 3.5. Differential number count is estimated in flux range between 3.5 and 9.0 mJy after applying various corrections derived by imaging simulations, which is consistent with previous studies. For detailed study on the individual sources, we select three sources with more reliable measurements (S/N > 4.5), and construct their spectral energy distributions (SEDs) from optical to far-infrared band. Redshift distribution of the sources ranges from 0.36 to 3.28, and their physical parameters are extracted using MAGPHYS model, which yield infrared luminosity $L_{IR}=10^{11.3}-10^{13.4}L_{\odot}$, star formation rate $SFR=10^{1.3}-10^{3.2}M_{\odot}yr^{-1}$ and dust temperature $T_D=30-53K$. We investigate the correlation between $L_{IR}$ and $T_D$, which appears to be consistent with previous studies.