• 호남수학학술지
• /
• 제6권1호
• /
• pp.1-12
• /
• 1984

Let(X, $\Im$) be a probabilistic metric space with a t-norm. Common fixed point theorems and convergence theorems generalizing the results of Ćirić, Fisher, Sehgal, Istrătescu-Săcuiu and others are proved for three mappings P,S,T on X satisfying $F_{Pu, Pv}(qx){\geq}min\left{F_{Su,Tv}(x),F_{Pu,Su}(x),F_{Pv,Tv}(x),F_{Pu,Tv}(2x),F_{Pv,Su}(2x)\right}$ for every $u, v {\in}X$, all x>0 and some $q{\in}(0, 1)$. One of the main results is extended to uniform spaces. Mathematics Subject Classification (1980): 54H25.

• Korean Journal of Mathematics
• /
• 제24권4호
• /
• pp.647-662
• /
• 2016

In this paper, we study Lipschitz continuous, the boundedness and compactness of the composition operator $C_{\phi}$ acting between the general hyperbolic Bloch type-classes ${\mathcal{B}}^{\ast}_{p,{\log},{\alpha}}$ and general hyperbolic Besov-type classes $F^{\ast}_{p,{\log}}(p,q,s)$. Moreover, these classes are shown to be complete metric spaces with respect to the corresponding metrics.

• Journal of applied mathematics & informatics
• /
• 제28권1_2호
• /
• pp.13-30
• /
• 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.

• Korean Journal of Mathematics
• /
• 제14권2호
• /
• pp.137-160
• /
• 2006

We describe the weight functions for which Hardy's inequality of nonincreasing functions is satisfied. Further we characterize the pairs of weight functions $(w,v)$ for which the Laplace transform $\mathcal{L}f(x)={\int}^{\infty}_0e^{-xy}f(y)dy$, with monotone function $f$, is bounded from the weighted Lebesgue space $L^p(w)$ to $L^q(v)$.

• 충청수학회지
• /
• 제21권4호
• /
• pp.437-445
• /
• 2008

We show the existence of at least four nontrivial critical points of the $C^{1,1}$ functional f on the Hilbert space $H=X_0{\oplus}X_1{\oplus}X_2{\oplus}X_3{\oplus}X_4$, $X_i$, i = 0, 1, 2, 3 are finite dimensional, with f(0) = 0 when two sublevel subsets, torus with three holes and sphere, of f link, the functional f satisfies sup-inf variatinal linking inequality on the linking subspaces, the functional f satisfies $(P.S.)_c$ condition, and $f{\mid}_{X_0{\oplus}X_4}$ has no critical point with level c. We use the deformation lemma, the relative category theory and the critical point theory for the proof of main result.

• Journal of Magnetics
• /
• 제19권2호
• /
• pp.126-129
• /
• 2014

We report the crystallographic and magnetic properties of $Ni_{0.3}Fe_{0.7}Ga_2S_4$ by means of X-ray diffractometer (XRD), a superconducting quantum interference device (SQUID) magnetometer, and a M$\ddot{o}$ssbauer spectroscopy. In particular, $Ni_{0.3}Fe_{0.7}Ga_2S_4$ was studied by M$\ddot{o}$ssbauer analysis for evidence of spin reorientation. The chalcogenide material $Ni_{0.3}Fe_{0.7}Ga_2S_4$ was fabricated by a direct reaction method. XRD analysis confirmed that $Ni_{0.3}Fe_{0.7}Ga_2S_4$ has a 2-dimension (2-D) triangular lattice structure, with space group P-3m1. The M$\ddot{o}$ssbauer spectra of $Ni_{0.3}Fe_{0.7}Ga_2S_4$ at spectra at various temperatures from 4.2 to 300 K showed that the spectrum at 4.2 K has a severely distorted 8-line shape, as spin liquid. Electric quadrupole splitting, $E_Q$ has anomalous two-points of temperature dependence of $E_Q$ curve as freezing temperature, $T_f=11K$, and N$\acute{e}$el temperature, $T_N=26K$. This suggests that there appears to be a slowly-fluctuating "spin gel" state between $T_f$ and $T_N$, caused by non-paramagnetic spin state below $T_N$. This comes from charge re-distribution due to spin-orientation above $T_f$, and $T_N$, due to the changing $E_Q$ at various temperatures. Isomer shift value ($0.7mm/s{\leq}{\delta}{\leq}0.9mm/s$) shows that the charge states are ferrous ($Fe^{2+}$), for all temperature range. The Debye temperature for the octahedral site was found to be ${\Theta}_D=260K$.

• 대한수학회보
• /
• 제46권2호
• /
• pp.311-319
• /
• 2009

Let H be a Hilbert space which is the direct sum of five closed subspaces $X_0,\;X_1,\;X_2,\;X_3$ and $X_4$ with $X_1,\;X_2,\;X_3$ of finite dimension. Let J be a $C^{1,1}$ functional defined on H with J(0) = 0. We show the existence of at least four nontrivial critical points when the sublevels of J (the torus with three holes and sphere) link and the functional J satisfies sup-inf variational inequality on the linking subspaces, and the functional J satisfies $(P.S.)^*_c$ condition and $f|X_0{\otimes}X_4$ has no critical point with level c. For the proof of main theorem we use the nonsmooth version of the classical deformation lemma and the limit relative category theory.

• 천문학회지
• /
• 제39권2호
• /
• pp.41-50
• /
• 2006

We present the results of new multi-color CCD photometry for the contact binary XZ Leo, together with reasonable explanations for the period and light variations. Six new times of minimum light have been determined. A period study with all available timings confirms Qian's (2001) finding that the O-C residuals have varied secularly according to $dP/dt\;=\;+8.20{\times}10^{-8}\;d\;yr^{-l}$. This trend could be interpreted as a conservative mass transfer from the less massive cool secondary to the more massive hot primary in the system with a mass flow rate of about $5.37{\times}10^{-8}\;M_{\odot}\;yr^{-l}$. By simultaneous analysis of our light curves and the previously published radial-velocity data, a consistent set of light and velocity parameters for XZ Leo is obtained. The small differences between the observed and theoretical light curves are modelled by a blue third light and by a hot spot near the neck of the primary component. Our period study does not support the tertiary light but the hot region which may be formed by gas streams from the cool secondary. The solution indicates that XZ Leo is a deep contact binary with the values of q=0.343, $i=78^{\circ}.8$, ${\Delta}(T_1-T_2)=126\;K$, and f=33.6 %, differing much from those of Niarchos et al. (1994). Absolute parameters of XZ Leo are determined as follows: $M_1=1.84\;M_{\odot},\;M_2=0.63\;M_{\odot},\;R_1=1.75\;R_{\odot},\;R_2=1.10\;R_{\odot},\;L_1=7.19\;L_{\odot},\;and\;L_2=2.66\;L_{\odot}$.