• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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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.

• Journal of computational fluids engineering
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• v.2 no.1
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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.

• The Pure and Applied Mathematics
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• v.30 no.1
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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.

• The Pure and Applied Mathematics
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• v.31 no.2
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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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• v.21 no.1
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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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• v.19 no.4
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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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• v.24 no.1
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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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• 1995.10a
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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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• v.29 no.1
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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.

• Environmental and Resource Economics Review
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• v.12 no.4
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• pp.637-661
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• 2003

This paper analyzes the impact of import liberalization of petroleum product market in 1997 on the behavior of a domestic industry, regarded as a typical oligopoly. Based on the theory of implicit cartel, two regression equations were formulated and estimated for domestic production and refinery margin using monthly data for the period from Jan. 1994 to June 2003. Estimation results show that not only did domestic production rise sharply but also the refining cost fell substantially throughout 1996 before the actual liberalization of imports, Such a response is clearly consistent with the implicit cartel theory, which suggests that once the difficulty of maintaining a cartel in the future is recognized, the cartel immediately collapses and anticipation of import liberalization can cause immediately lowering market price as well as an immediate expansion of the supply by a domestic industry. However, the significant reduction of refinery cost accompanied by a large contraction in domestic output after the actual implementation of import liberalization can be explained by the collapse of implicit cartel caused by the anticipated liberalization of imports. Thus, import liberalization in the sense of allowing entry of foreign producers into domestic market has seemed to be an effective means to weaken market power and induce more competitive conduct of domestic firms.