• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.209-224
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• 2024

The goal of this study is to instigate various new and novel optimum proximity point theorems using the notion of implicit relation type ℶ-proximal contraction for non-self mappings. An illustrated example is used to demonstrate the validity of the obtained results. Furthermore, some uniqueness results for proximal contractions are also furnished with partial order and graph. Various well-known discoveries in the present state-of-the-art are enhanced, extended, unified, and generalized by our findings. As an application, we generate some fixed point results fulfilling a modified contraction and a graph contraction, using the profundity of the established results.

• 한국전산유체공학회지
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• 제2권1호
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• pp.8-12
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• 1997

The three-dimensional Euler equations are solved numerically for the analysis of contraction flows in wind or water tunnels. A second-order finite difference method is used for the spatial discretization on the nonstaggered grid system and the 4-stage Runge-Kutta scheme for the numerical integration in time. In order to speed up the convergence, the local time stepping and the implicit residual-averaging schemes are introduced. The pressure field is obtained by solving the pressure-Poisson equation with the Neumann boundary condition. For the evaluation of the present Euler solver, numerical computations are carried out for three contraction geometries, one of which was adopted in the Large Cavitation Channel for the U.S. Navy. The comparison of the computational results with the available experimental data shows good agreement.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권1호
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• pp.25-34
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• 2023

Popa [14] proved the common fixed point theorem using implicit relations. Saluja [17] proved a fixed point theorem on complete partial metric spaces satisfying an implicit relation. In this paper, we prove a fixed point theorem on complete partial metric space satisfying another implicit relation.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제31권2호
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• pp.217-233
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• 2024

In this paper we study a tripled quasi-metric with new fixed point theorems around β-implicit contractions in tripled quasi-metric spaces. We give an example on a solution of a integral equations.

• East Asian mathematical journal
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• 제21권1호
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• pp.65-76
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• 2005

In this paper the concept of semi-compatibility has been introduced in Menger space and it has been applied to prove results on existence of unique common fixed point of four self maps satisfying an implicit relation. It results in a generalization of Banach contraction principle established by Sehgal and Bharucha-Reid in [8] All the result presented in this paper are new.

• Korea-Australia Rheology Journal
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• 제19권4호
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• pp.211-219
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• 2007

Here we demonstrate complex transient behavior of viscoelastic liquid described numerically with the Leonov model in straight and contraction channel flow domains. Finite element and implicit Euler time integration methods are employed for spatial discretization and time marching. In order to stabilize the computational procedure, the tensor-logarithmic formulation of the constitutive equation with SUPG and DEVSS algorithms is implemented. For completeness of numerical formulation, the so called traction boundaries are assigned for flow inlet and outlet boundaries. At the inlet, finite traction force in the flow direction with stress free condition is allocated whereas the traction free boundary is assigned at the outlet. The numerical result has illustrated severe forward-backward fluctuations of overall flow rate in inertial straight channel flow ultimately followed by steady state of forward flow. When the flow reversal occurs, the flow patterns exhibit quite complicated time variation of streamlines. In the inertialess flow, it takes much more time to reach the steady state in the contraction flow than in the straight pipe flow. Even in the inertialess case during startup contraction flow, quite distinctly altering flow patterns with the lapse of time have been observed such as appearing and vanishing of lip vortices, coexistence of multiple vortices at the contraction comer and their merging into one.

• East Asian mathematical journal
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• 제24권1호
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• pp.81-95
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• 2008

Let E be a uniformly convex Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm, C a nonempty closed convex subset of E, and $T\;:\;C\;{\rightarrow}\;E$ a nonexpansive mapping satisfying the weak inwardness condition. Assume that every weakly compact convex subset of E has the fixed point property. For $f\;:\;C\;{\rightarrow}\;C$ a contraction and $t\;{\in}\;(0,\;1)$, let $x_t$ be a unique fixed point of a contraction $T_t\;:\;C\;{\rightarrow}\;E$, defined by $T_tx\;=\;tf(x)\;+\;(1\;-\;t)Tx$, $x\;{\in}\;C$. It is proved that if {$x_t$} is bounded, then $x_t$ converges to a fixed point of T, which is the unique solution of certain variational inequality. Moreover, the strong convergence of other implicit and explicit iterative schemes involving the sunny nonexpansive retraction is also given in a reflexive and strictly convex Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 1995년도 추계 학술대회논문집
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• pp.175-181
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• 1995

Three-Dimensional Euler equations are solved numerically for the analysis of contraction flows in wind or water tunnels. A second-order finite difference method is used for the spatial discretization on the nonstaggered grid system and the 4-stage Runge-Kutta scheme for the numerical integration in time. In order to speed up the convergence, the local time stepping and the implicit residual-averaging schemes are introduced. The pressure field is obtained by solving the pressure-Poisson equation with the Neumann boundary condition. For the evaluation of the present Euler solver, numerical computations are carried out for the various contraction geometries, one of which was adopted in the Large Cavitation Channel for the U.S. Navy. The comparison of the computational results with the available experimental data shows good agreements.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.113-130
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• 2024

In this work, we explore the existence and uniqueness results for a class of boundary value issues for implicit Volterra-Fredholm nonlinear integro-differential equations (IDEs) with Atangana-Baleanu-Riemann fractional (ABR-fractional) that have non-instantaneous multi-point fractional boundary conditions. The findings are supported by Krasnoselskii's fixed point theorem, Gronwall-Bellman inequality, and the Banach contraction principle. Finally, a demonstrative example is provided to support our key findings.

• 자원ㆍ환경경제연구
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• 제12권4호
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• pp.637-661
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• 2003

본 연구는 1997년 정부의 석유제품 수입자유화 조치가 전형적인 과점기업인 국내 석유기업들의 시장행위에 미친 영향을 분석하고자 하였다. 이를 위해 암묵적 카르텔 이론을 기초로 두 가지 지표, 즉 공급량과 정제마진(정제비용과 이윤의 합)에 반영된 국내 석유기업들의 시장형태를 1994년부터 2003년 6월까지의 월별 자료를 이용해 추정하였다. 추정결과는, 수입자유화가 예상되는 시기부터 이미 국내 석유기업들의 공급량은 크게 증가하는 반면 정제마진은 감소하는 현상이 통계적으로 매우 유의적으로 나타나, 국내 석유기업들이 자유화 이전에 암묵적 협조체제를 형성하고 있었을 가능성이 높게 나타났다. 한편 2000년 이후 국내 석유기업들의 공급량은 외환위기 때의 수준을 유지하고 있는 반면 정제마진은 수입자유화 이전에 비해 큰 폭으로 하락한 것으로 나타났으며, 제품별로는 특히 휘발유의 정제마진이 타제품에 비해 통계적으로 가장 유의성 있게 큰 폭으로 하락한 것으로 나타났다. 이는 수입자유화의 영향이 본격적으로 나타나기 시작한 2000년 이후부터 국내시장에서는 모든 석유제품을 대상으로 시장경쟁이 치열함을 입증하는 것으로서, 현재 국내 정유사들의 가격결정이 상호 협조 속에서 이루어지고 있다고 보기는 어렵다. 따라서 정부의 수입자유화 조치는 국내 석유기업들의 시장행위에 큰 영향을 주어 국내 석유제품시장의 구조를 암묵적 협조체제에서 비협조적 경쟁시장으로 만드는 계기가 된 것으로 볼 수 있다.