• Honam Mathematical Journal
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• v.45 no.1
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• pp.1-24
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• 2023

In the present paper, we prove common fixed point theorems for a pair of weakly compatible mappings under implicit contractive relation in quasi-partial S_b-metric spaces. We also provide an illustrative example to support our results. Furthermore, we will use the results obtained for application to two boundary value problems for the second-order differential equation. Also, we prove a common solution for the nonlinear fractional differential equation.

• 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.

• Honam Mathematical Journal
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• v.38 no.2
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• pp.213-229
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• 2016

In this paper, we utilize an implicit relation to improve and extend some strict common fixed point results of the existing literature to two pairs of hybrid mappings in 2-metric spaces via altering distances. As an application, we also prove some strict common fixed point theorems for hybrid pairs of mappings satisfying a contractive condition of integral type in 2-metric spaces.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.1839-1854
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• 2015

Brief developments in metrical fixed point theory are covered and a significant generalization of recent results obtained in [18], [27], [32] and [33] is established through an extension of the property (EA) to two sequences of self-maps using the notions of weak compatibility and implicit relation.

• Journal of Korea Multimedia Society
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• v.8 no.2
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• pp.249-257
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• 2005

This paper aims at reducing aliasing in pixel-based rendering for 3D implicit surfaces by shifted multi Z-buffers. The voxelized implicit surfaces with high resolution take so much time in generating high Quality image without aliasing. So in rendering a voxelized implicit surfaces, a new antialiasing method which can generate a high quality image at a lower resolution is required. Therefore, this paper suggests that a method which get various sampling values by shifting several z-buffers in each voxel and average them, The advantages are effective memory, simple calculation and easy convergence with various filters. But, the increase of number of z-buffer also increase the consuming time rapidly. Therefore, the research for representing the relation the degree of image quality with the consumption of time as a number is required.

• Journal of electromagnetic engineering and science
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• v.3 no.1
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• pp.39-44
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• 2003

An unconditionally stable compact 2D Alternating-Direction Implicit (ADI) FDTD method for calculating dispersion characteristics of waveguide structures is proposed. The numerical stability and numerical dispersion relation of the proposed method are also presented and discussed. Numerical wavelengths for the dominant and higher order modes in a hollow waveguide are obtained from numerical simulations and compared with those from the analytical dispersion relation. The numerical results show that the proposed scheme has the potential to successfully analyze a class of waveguides having locally fine geometry with reduced numerical costs.

• 한국노년학
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• v.38 no.3
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• pp.409-433
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• 2018

The purpose of this study is to examine the effect of contact with the elderly in a daily life on children's ageist attitude. Acknowledging the people's tendency to report in socially appropriate ways to the explicit attitude measurement, implicit measurement is introduced, and relation with the daily contact with elderly(DCE) is analyzed. The research question are as follows: 1) Are these two attitudes explained by different factors? 2) Can DCE alleviate both children's implicit and explicit ageist attitude? 3) How do the contact with grandparent and neighboring elderly affect the children's explicit and implicit ageist attitude? Data was collected from 503 fourth to sixth grade elementary school children. Child-Age Implict Association Test is used to measure implicit ageist attitude. Multinominal logistic analysis and ordered logistic analysis was applied. Followings are the main results: First, explicit and implicit ageist attitudes are found to be related with different predictors. Second, Elderly contact seems to lighten children's ageist attitude overall. Third, the effects of grandparental contact and the neighboring elderly contact on two different ageism were different. While the effect of elderly neighbor contact is limited to the expression of ageism, grandparental contact has a influence not only on the explicit but also on the implicit ageism, even though the effect on implicit attitude is limited in extent. Forth, not the quality of contact but the quantity of it was related to implicit ageist attitude. This result contradicts conventional idea of Intergroup Contact Theory. In the further research, the predictor of implicit ageist attitude need to be throughly examined.

• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.41-55
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• 2009

A general common fixed point theorem for two pairs of weakly compatible mappings using an implicit function is proved without any continuity requirement which generalizes the result due to Popa [20, Theorem 3]. In process, several previously known results due to Fisher, Kannan, Jeong and Rhoades, Imdad and Ali, Imdad and Khan, Khan, Shahzad and others are derived as special cases. Some related results and illustrative examples are also discussed. As an application of our main result, we prove an existence theorem for the solution of simultaneous Hammerstein type integral equations.

• The Pure and Applied Mathematics
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• v.15 no.1
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• pp.85-92
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• 2008

In topoi, there are various forms of the axiom of choice such as (ES), (AC) and (WO). And also there are various weak forms of the axiom of choice such as (DES), (IAC) and (ASC). First we investigate the relation between (IAC) and (ASC), and then we study the relation between (AC) and (WO). We get equivalent forms of the axiom of choice in a well-pointed topos.