• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제27권3호
• /
• pp.160-179
• /
• 2023

In this paper, we investigate the existence and diameter of the approximate fixed point results on E-metric spaces (not necessarily complete) by using various cyclic contraction mappings, including the B-cyclic contraction, the Bianchini cyclic contraction, the Hardy-Rogers cyclic contraction, and so on. Additionally, we prove the approximate fixed point results for rational type cyclic contraction mappings, which were discussed mainly in [35] and [37], in the setting of E-metric space. Also, a few examples are provided to demonstrate our findings. Subsequently, we discuss some applications of approximate fixed point results in the field of applied mathematics rigorously.

• 대한수학회보
• /
• 제34권3호
• /
• pp.385-394
• /
• 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.

• 대한수학회지
• /
• 제42권5호
• /
• pp.1087-1100
• /
• 2005

In this note we give the mapping properties of the Marcinkiewicz integral !-to. at some end spaces. More precisely, we first prove that !-to. is a bounded operator from H$^{1,($\mathbb{R) to H$^{1, ($\mathbb{R). As a corollary of the results above, we obtain again the weak type (1,1) boundedness of $\mu$$_{, but the condition assumed on n is weaker than Stein's condition. Finally, we show that !-to. is bounded from BMO($\mathbb{R) to BMO($\mathbb{R). The results in this note are the extensions of the results obtained by Lee and Rim recently.

• 동력기계공학회지
• /
• 제4권3호
• /
• pp.72-80
• /
• 2000

In order to design a stable robust controller, nominal model, and the upper bound about the uncertainty which is the error of the model are needed. The problem to estimate the nominal model of controlled system and the upper bound of uncertainty at the same time is called robust identification. When the nominal model of controlled system and the upper bound of uncertainty in relation to robust identification are given, the evaluation of the validity of the model and the upper bound makes it possible to distinguish whether there is a model which explains observation data including disturbance among the model set. This paper suggests a method to identity the uncertainty which removes disturbance and expounds observation data by giving a probable postulation and plural data set to disturbance. It also examines the suggested method through a numerical computation simulation and validates its effectiveness.

• 대한수학회보
• /
• 제52권5호
• /
• pp.1729-1735
• /
• 2015

It is known that the partial sum of the Taylor series of an holomorphic function of one complex variable converges in norm on $H^p(\mathbb{D})$ for 1 < p < ${\infty}$. In this paper, we consider various type of partial sums of a holomorphic function of several variables which also converge in norm on $H^p(\mathbb{B}_n)$ for 1 < p < ${\infty}$. For the partial sums in several variable cases, some variables could be chosen slowly (fastly) relative to other variables. We prove that in any cases the partial sum converges to the original function, regardlessly how slowly (fastly) some variables are taken.

• Korean Journal of Geomatics
• /
• 제5권1호
• /
• pp.1-6
• /
• 2005

When merging various datasets the perennial problem of relative weighting arises. In case of two datasets an iterative algorithm has been developed recently that allows the rigorous determination of optimal variance components of type repro-BIQUUE even for large amounts of data, along with the estimation of the joint parameters. Here we shall present this new algorithm, and show its versatility in an example that will entail the merging of two regional geoid estimates (derived from EGM 96 and CHAMP) in terms of certain series expansions which have been proven previously to belong to the most efficient ones (e.g., wavelets, Hardy's multi-quadrics, etc.). Future attempts will be devoted to the sequential merging of altimeter and tide gauge data.

• 대한수학회보
• /
• 제53권2호
• /
• pp.561-568
• /
• 2016

In this paper, the effect of absolute values on the behavior of functions f in the spaces $\mathcal{Q}_K$ is investigated. It is clear that $g{\in}\mathcal{Q}_K({\partial}{\mathbb{D}}){\Rightarrow}{\mid}g{\mid}{\in}\mathcal{Q}_K({\partial}{\mathbb{D}})$, but the converse is not always true. For f in the Hardy space $H^2$, we give a condition involving the modulus of the function only, such that the condition together with ${\mid}f{\mid}{\in}\mathcal{Q}_K({\partial}{\mathbb{D}})$ is equivalent to $f{\in}\mathcal{Q}_K$. As an application, a new criterion for inner-outer factorisation of $\mathcal{Q}_K$ spaces is given. These results are also new for $Q_p$ spaces.

• 한국터널지하공간학회 논문집
• /
• 제19권2호
• /
• pp.213-229
• /
• 2017

최근 도심지 터널은 진출입 Ramp를 포함한 다양한 형태의 네트워크형 터널이 건설되고 있다. 더불어 터널환기 해석을 위한 다양한 네트워크 이론 기반의 1D 프로그램들이 개발되고 있다. 본 연구에서는 비 hardy-cross 법에 기초한 네트워크형 터널에 대한 풍량 및 농도해석이 가능한 프로그램을 개발하였다. 터널 구간내 풍량해석은 Gradient 법에 기초하고 있으며, 농도해석을 위하여 복잡한 네트워크 구조에서 유입과 유출농도를 자동계산 할 수 있는 로직을 개발하였고, 저속풍량구간에서는 수치해석적 오차를 축소시키기 위한 적정 그리드 간격을 제시하였다. 또한, 프로그램의 적정성을 검증하기 위해, 일자형 터널을 대상으로 고전적인 Sokic의 풍속 선도법 및 TVSDM 프로그램과의 풍속비교검증을 수행하였으며 오차율은 1% 이하였다. 또한 최근 건설되는 도심지 터널에 적용중인 최신 환기방식에 대한 네트워크 환기해석을 수행하였다.