• 한국수학교육학회지시리즈B:순수및응용수학
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• 제27권4호
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• pp.187-205
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• 2020

In this article, we prove coincidence point theorems for comparable 𝜓-contractive mappings in ordered non-Archimedean fuzzy metric spaces utilizing the recently established concept of 𝓣-comparability and relatively weaker order theoretic variants. With a view to show the usefulness and applicability of this work, we solve the system of ordered Fredholm integral equations as an application. In the process, this presentation generalize and improve some prominent recent results obtained in Mihet [Fuzzy Sets Syst., 159 (6), 739-744, (2008)], Altun and Mihet [ Fixed Point Theory Appl. 2010, 782680, (2010)], Alam and Imdad [Fixed Point Theory, 18(2), 415-432, (2017)] and several others in the settings of partially ordered non-Archimedean fuzzy metric spaces.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제28권3호
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• pp.253-266
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• 2021

In this paper, we generalize the notion of comparable set-valued mappings by introducing two types of 𝓡-closed set-valued mappings and utilize these to obtain an analogue of celebrated Mizoguchi and Takahashi fixed point theorem in relational metric spaces. To annotate the claims and usefulness of such findings, we prove fixed point results for both set-valued and single-valued mappings and validate the assertions with the help of examples. In this way, these investigations extend, modify and generalize some prominent recent fixed point results obtained by Tiammee and Suantai [24], Amini-Harandi and Emami [4], Prasad and Dimri [19] and several others in the settings of relational metric spaces.

• 대한수학회논문집
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• 제28권1호
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• pp.107-121
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• 2013

The purpose of this paper is to investigate the demiclosed principle, the existence theorems and convergence theorems in CAT(0) spaces for a class of mappings which is essentially wider than that of asymptotically nonexpansive mappings. The structure of fixed point set of such mappings is also studied. Our results generalize, unify and extend several comparable results in the existing literature.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제23권2호
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• pp.131-143
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• 2016

In this paper, we present some common fixed point theorems for two pairs of weakly compatible self-mappings on multiplicative metric spaces satisfying a generalized Meir-Keeler type contractive condition. The results obtained in this paper extend, improve and generalize some well known comparable results in literature.

• 대한수학회논문집
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• 제32권2호
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• pp.375-387
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• 2017

In this paper, we prove some coincidence point theorems involving ${\varphi}-contraction$ in ordered partial metric spaces. We also extend newly introduced notion of g-comparability of a pair of maps for linear contraction in ordered metric spaces to non-linear contraction in ordered partial metric spaces. Thus, our results extend, modify and generalize some recent well known coincidence point theorems of ordered metric spaces.

• Nonlinear Functional Analysis and Applications
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• 제26권5호
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• pp.971-983
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• 2021

In this paper, we prove common fixed point theorems for six weakly compatible mappings in G-fuzzy metric spaces introduced by Sun and Yang [16] which is actually generalization of G-metric spaces. G-metric spaces coined by Mustafa and Sims [13]. The paper concerns our sustained efforts for the materialization of G-fuzzy metric spaces and their properties. We also exercise the concept of symmetric G-fuzzy metric space, 𝜙-function and weakly compatible mappings. The results present in this paper generalize the well-known comparable results in the literature. We justify our results by suitable examples. Some applications are also given in support of our results.

• Kyungpook Mathematical Journal
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• 제55권1호
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• pp.205-218
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• 2015

In this paper, we introduce the concept of generalized c-distance on a cone metric space and prove some common fixed point and coincidence point results by using this notion. Our results generalize and extend several well known comparable results in the literature.

• 대한기계학회논문집A
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• 제31권12호
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• pp.1200-1207
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• 2007

An experimental test is presented for photoelastic stress analysis around a crack tip in tensile loaded plate. The hybrid method coupling photoelastsic fringe inputs calculated by finite element method and complex variable formulations involving conformal mappings and analytical continuity is used to calculate full-field stress around the crack tip in uniaxially loaded, finite width tensile plate. In order to accurately compare calculated fringes with experimental ones, both actual and regenerated photoelastic fringe patterns are two times multiplied and sharpened by digital image processing. Regenerated fringes by hybrid method are quite comparable to actual fringes. The experimental results indicate that Mode I stress intensity factor analyzed by the hybrid method are accurate within three percent compared with ones obtained by empirical equation and finite element analysis.

• 한국정밀공학회지
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• 제25권10호
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• pp.84-91
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• 2008

Due to the complexity of the engineering problems, it is difficult to obtain directly the stress field around the crack tip by theoretical derivation. In the paper, the hybrid method is employed to calculate full-field stress around the crack tip in uni-axially leaded finite width tensile plate, using the displacement data of given points calculated by finite element method as input data. The method uses complex variable formulations involving conformal mappings and analytical continuity. In order to accurately compare calculated fringes with experimental ones, both actual and reconstructed photoelastic fringe patterns are two times multiplied and sharpened by digital image processing. Reconstructed fringes by hybrid method are quite comparable to actual fringes. The experimental results indicate that Mode I stress intensity factor analyzed by the hybrid method are accurate within a few percent compared with ones obtained by empirical equation and finite element analysis.

• 한국진공학회:학술대회논문집
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• 한국진공학회 2009년도 제38회 동계학술대회 초록집
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• pp.12-12
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• 2010

By using scanning tunneling microscopy/spectroscopy (STM/S), we can make images of various physical properties in nanometer-scale spatial resolutions. Here, I demonstrate imaging of two electron-correlated subjects; screening and superconductivity by STM/S. The electrostatic potential around a charge is described with the Coulomb potential. When the charge is located in a metal, the potential is modified because of the free electrons in the host. The potential modification, called screening, is one of the fundamental phenomena in the condensed matter physics. Using low-temperature STM we have developed a method to measure electrostatic potential in high spatial and energy resolutions, and observed the potential around external charges screened by two-dimensional surface electronic states. Characteristic potential decay and the Friedel oscillation were clearly observed around the charges [1]. Superconductivity of nano-size materials, whose dimensions are comparable with the coherence length, is quite different from their bulk. We investigated superconductivity of ultra-thin Pb islands by directly measuring the superconducting gaps using STM. The obtained tunneling spectra exhibit a variation of zero bias conductance (ZBC) with a magnetic field, and spatial mappings of ZBC revealed the vortex formation [2]. Size dependence of the vortex formation will be discussed at the presentation.