• The Pure and Applied Mathematics
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• v.29 no.4
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• pp.369-399
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• 2022

In the last few decades, a lot of generalizations of the Banach contraction principle have been introduced. In this paper, we present the notion of (𝜙, F)-contraction in generalized asymmetric metric spaces and we investigate the existence of fixed points of such mappings. We also provide some illustrative examples to show that our results improve many existing results.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1201-1222
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• 2019

In this paper, we introduce the notion of modified TAC-Suzuki-Berinde type F-contraction and modified TAC-(${\psi}$, ${\phi}$)-Suzuki type rational mappings in the frame work of complete metric spaces, we also establish some fixed point results regarding this class of mappings and we present some examples to support our main results. The results obtained in this work extend and generalize the results of Dutta et al. [9], Rhoades [18], Doric, [8], Khan et al. [13], Wardowski [25], Piri et al. [17], Sing et al. [23] and many more results in this direction.

• Honam Mathematical Journal
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• v.30 no.1
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• pp.197-203
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• 2008

We show the existence of the unique solution of the following system of the nonlinear wave equations with Dirichlet boundary conditions and periodic conditions under some conditions $U_{tt}-U_{xx}+av^+=s{\phi}_{00}+f$ in $(-{\frac{\pi}{2},{\frac{\pi}{2}}){\times}R$, ${\upsilon}_{tt}-{\upsilon}_{xx}+bu^+=t{\phi}_{00}+g$ in $(-{\frac{\pi}{2},{\frac{\pi}{2}}){\times}R$, where $u^+$ = max{u, 0}, s, t ${\in}$ R, ${\phi}_{00}$ is the eigenfunction corresponding to the positive eigenvalue ${\lambda}_{00}$ of the wave operator. We first show that the system has a positive solution or a negative solution depending on the sand t, and then prove the uniqueness theorem by the contraction mapping principle on the Banach space.

• Journal of the Optical Society of Korea
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• v.2 no.2
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• pp.74-79
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• 1998

The use of a fiber Fabry-Perot interferometer (FFPI) as an optical current transducer is demonstrated. A conventional inductive pickup coil converts the time-varying current I(t) being measured to a voltage waveform V(t) applied across a piezeolectric strip to which the FFPI is bonded. The strip experiences a longitudinal expansion and contraction, resulting in an optical phase shift ${\phi}(t)$ in the fiber proportional to V(t). This phase shift is measured using a frequency-modulated semiconductor light source, photodiodes to monitor the reflected light from the FFPI and the laser power, and a digital signal processor. Calibration routines compute V(t) and I(t) from the measured phase shift at a l KHz rate. Response to 60 Hz ac over the design range 0-1300A rms is characterized Transient response of the FFPI transducer is also measured.