• Communications of the Korean Mathematical Society
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• v.31 no.1
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• pp.139-145
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• 2016

In this paper, some new fixed point theorems for condensing mappings are established based on a well known result of Petryshyn. We use several Leray-Schauder type conditions to prove new fixed point results. We also obtain generalizations of Altman's theorem and Petryshyn's theorem as well.

• Tribology and Lubricants
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• v.16 no.6
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• pp.432-439
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• 2000

The present work is an attempt to calculate the steady state pressure and perturbed pressure of herringbone grooved journal bearings. A generalized coordinate system is introduced to handle the complex bearing geometry. The coordinates are fitted to the groove boundary and the Reynold's equation is transformed to be fitted to this coordinate system using the Gauss divergence theorem. This method makes it possible to deal with an arbitrary configuration of a lubricated surface. The caharacteristics of finite herringbone groove journal bearing are well calculated using this method.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.351-358
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• 2014

In this paper, under some suitable integrability and smoothness conditions on f, we establish the central limit theorems for $$\sum_{k{\leq}N}k^{-1}f(S_k/{\sigma}\sqrt{k})$$, where $S_k$ is the partial sums of strictly stationary mixing random variables with $EX_1=0$ and ${\sigma}^2=EX^2_1+2\sum_{k=1}^{\infty}EX_1X_{1+k}$. We also establish an almost sure limit behaviors of the above sums.

• Korean Journal of Mathematics
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• v.8 no.2
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• pp.127-134
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• 2000

Motivated by recent work of Uralegaddi and Sarangi[12], we aim at presenting here system study of novel subclass $R_{\alpha}[{\mu},{\beta},{\xi}]$ of prestarlike functions. Further using operators of fractional calculus, we have obtained distortion theorem for $R_{\alpha}[{\mu},{\beta},{\xi}]$. Lastly the extreme points of $R_{\alpha}[{\mu},{\beta},{\xi}]$ are obtained.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.725-737
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• 1995

Let $X_t = (X_t^(1), X_t^(2))', t \geqslant 0$, be a real stationary 2-dimensional Gaussian process with $EX_t^(1) = EX_t^(2) = 0$ and $$ EX_0 X'_t = (_{\rho(t) r(t)}^{r(t) \rho(t)}), $$ where $r(t) \sim $\mid$t$\mid$^-\alpha, 0 < \alpha < 1/2, \rho(t) = o(r(t)) as t \to \infty, r(0) = 1, and \rho(0) = \rho (0 \leqslant \rho < 1)$. For $t > 0, u > 0, and \upsilon > 0, let L_t (u, \upsilon)$ be the time spent by $X_s, 0 \leqslant s \leqslant t$, above the level $(u, \upsilon)$.

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.385-392
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• 1996

Smale [16] posed the following question; is having an attracting periodic orbit a generic property for diffeomorphisms of two-sphere $S^2\ulcorner$(A generic property of $f \in Diff(M)$ is one that is true for a Baire set in Diff(M)). Mane[5] and Plykin[13] had an positive answer for Axiom A diffeomorphisms of $S^2$. To explain our theorem, we begin by briefly recalling stability conjecture posed by palis and smale.

• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.421-430
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• 2011

By evaluating the containment measure of one domain to contain another, we will derive some new Bonnesen-type inequalities (Theorem 2) via the method of integral geometry. We obtain Ren's sufficient condition for one domain to contain another domain (Theorem 4). We also obtain some new geometric inequalities. Finally we give a simplified proof of the Bottema's result.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.125-144
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• 2017

Three nontrivial nonnegative solutions for some critical quasilinear elliptic systems with lower-order negative perturbations are obtained by using the Ekeland's variational principle and the mountain pass theorem.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.881-888
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• 2001

Recently, Hooda and Ram [7] have proposed and characterized a new generalized measure of R-norm entropy. In the present communication we have studied its application in coding theory. Various mean codeword lengths and their bounds have been defined and a coding theorem on lower and upper bounds of a generalized mean codeword length in term of the generalized R-norm entropy has been proved.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.1041-1044
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• 2005

Recently, Zhang et al.(Fuzzy Sets and Systems 147(2004) 475-485) proved Fatou's lemma and Lebesgue dominated convergence theorem under some conditions of fuzzy measure. In this note, we show that these conditions of fuzzy measure is essential to prove Fatou's lemma and Lebesgue dominated convergence theorem by examples