• Nonlinear Functional Analysis and Applications
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• 제28권2호
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• pp.311-335
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• 2023

Fixed point theory is the center of focus for many mathematicians from last few decades. A lot of generalizations of the Banach contraction principle have been established. In this paper, we introduce the concepts of 𝜃-contraction and 𝜃-𝜑-contraction in quasi-metric spaces to study the existence of the fixed point for them.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제29권4호
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• pp.335-352
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• 2022

In this paper, we give an extended version of fixed point results for 𝜃-contraction and 𝜃-𝜙-contraction and define a new type of contraction, namely, cyclic 𝜃-contraction and cyclic 𝜃-𝜙-contraction in a complete metric space. Moreover, we prove the existence of best proximity point for cyclic 𝜃-contraction and cyclic 𝜃-𝜙-contraction. Also, we establish best proximity result in the setting of uniformly convex Banach space.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제26권3호
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• pp.111-131
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• 2019

We introduce (CLRg) property for hybrid pair $F:X{\times}X{\rightarrow}2^X$ and $g:X{\rightarrow}X$. We also introduce joint common limit range (JCLR) property for two hybrid pairs $F,G:X{\times}X{\rightarrow}2^X$ and $f,g:X{\rightarrow}X$. We also establish some common coupled fixed point theorems for hybrid pair of mappings under generalized (${\psi},{\theta},{\varphi}$)-contraction on a noncomplete metric space, which is not partially ordered. It is to be noted that to find coupled coincidence point, we do not employ the condition of continuity of any mapping involved therein. As an application, we study the existence and uniqueness of the solution to an integral equation. We also give an example to demonstrate the degree of validity of our hypothesis. The results we obtain generalize, extend and improve several recent results in the existing literature.

• The Journal of Korean Physical Therapy
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• 제24권2호
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• pp.127-133
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• 2012

Purpose: This study aims to examine the power changes in eletrocenphalogram (EEG) detected from the tibialis anterior muscle, during repetitive contraction exercise in normal female adults. Methods: The subjects of this study were 24 normal adult females, with no musculoskeletal or nervous system disorders. The 24 female subjects were divided into two groups: 12 subjects comprised a voluntary stimulation training group, and the other 12 subjects comprised an electrical stimulation training group. A total of thirty contractions were made repetitively by each woman, with maximal voluntary contraction exercise for six seconds, and a resting time of three seconds. During the experiment, their EEG was measured at eight positions. The eight positions were Fpz, Fz, Cz, CPz, C3, C4, P3, and P4, in accordance with the international 10~20 system. Results: The relative alpha power and beta power showed no statistically significant differences between the two groups. But the relative gamma power of the CPz, C3, C4, P3, and P4 areas showed statistically significant differences between the two groups (p<0.05). The relative theta power of the C4 area showed statistically significant differences between the two groups (p<0.05). Conclusion: Our findings show that tibialis anterior muscle contraction by electrical stimulation and by voluntary repeated contraction differentially affected brain activation. In particular, the CPz, C3, C4, P3 positions of relative gamma power showed brain activation in voluntary contraction. The C4 position of relative theta power showed different brain activation between the two groups.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제27권4호
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• pp.207-229
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• 2020

We establish fixed point and multidimensional fixed point results satisfying generalized (𝜓, 𝜃, 𝜑)-contraction on partially ordered non-Archimedean fuzzy metric spaces. By using this result we obtain the solution for periodic boundary value problems and give an example to show the degree of validity of our hypothesis. Our results generalize, extend and modify several well-known results in the literature.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제29권4호
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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.

• 호남수학학술지
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• 제40권4호
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• pp.719-732
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• 2018

In this manuscript, hybrid fixed point results for four maps using (E.A) and tangential properties in the setting of metric space are studied. Application to system of functional equations is also studied.

• 대한수학회보
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• 제52권6호
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• pp.1901-1910
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• 2015

In the present paper, considering the Jleli and Samet's technique we give many fixed point results for multivalued mappings on complete metric spaces without using the Pompeiu-Hausdorff metric. Our results are real generalization of some related fixed point theorems including the famous Feng and Liu's result in the literature. We also give some examples to both illustrate and show that our results are proper generalizations of the mentioned theorems.

• 폴리머
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• 제31권2호
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• pp.98-104
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• 2007

다양한 분자량의 폴리스티렌을 벤젠/n-헵탄, 1,4-다이옥산/이소프로판올, 1,4-다이옥산/n-헵탄과 같은 3종류의 혼합용매 계에 녹인 뒤 온도 상승에 따른 사슬의 팽창거동을 Flory $\Theta$온도 이상에서 점성도법으로 측정하였다. 온도 상승에 따라 두 종류의 영역, 즉 고분자 사슬이 팽창하는 영역과 수축하는 영역으로 구별되며, 분자량이 클수록 최대팽창온도가 높게 나타났다. 하나의 혼합용매 계 내에서는 $\tau/\tau_c$ 파라미터로 서로 다른 분자량의 사슬 팽창에 대하여 만능성이 나타나지만 서로 다른 혼합용매 계 사이에서는 각각의 기울기를 보임으로써 만능성이 관찰되지 않았다. 그러나 새로운 실험적 $b^{2/3}\tau/\tau_c$ 파라미터를 도입할 경우 모든 혼합용매 계의 사슬 팽창의 데이터들은 하나의 직선 위에 놓임으로써 만능성은 다시 회복되었다. 여기서 $\tau$는 $(T-\Theta)/\Theta$로 $\tau_c$는 $(\Theta-T_c)/T_c$로 각각 정의되며, $T_c$는 임계용액온도를 의미하며, b는 Schultz-Flory 식에서 $1/T_c$의 $1/M_w^{1/2}$에 대한 유효 기울기이다.