• Title, Summary, Keyword: ${\theta}$-contraction

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COMMON COUPLED FIXED POINT RESULTS FOR HYBRID PAIR OF MAPPING UNDER GENERALIZED (𝜓, 𝜃, 𝜑)-CONTRACTION WITH APPLICATION

  • Handa, Amrish
    • The Pure and Applied Mathematics
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    • v.26 no.3
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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.

Changes of Electroencephalogram according to Contraction Training Methods of Tibialis Anterior Muscle in Healthy Women (정상 여성에게서 앞 정강근의 수축훈련방법에 따른 뇌파의 변화)

  • Lee, Jeong-Woo;Kim, Moon-Jeong;Yoon, Se-Won
    • The Journal of Korean Physical Therapy
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    • v.24 no.2
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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.

ON FIXED POINT THEOREMS FOR MULTIVALUED MAPPINGS OF FENG-LIU TYPE

  • ALTUN, ISHAK;MINAK, GULHAN
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.6
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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.

Application of a New Scaling Parameter to Chain Expansion in the Systems of Polystyrene/Mixed Solvents (폴리스티렌/혼합용매 계에서 사슬의 팽창에 대한 새로운 스케일링 파라미터의 적용)

  • Park, Il-Hyun;Lee, Dong-Il;Hwang, Mi-Ok;Yu, Young-Chol;Park, Ki-Sang
    • Polymer(Korea)
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    • v.31 no.2
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    • pp.98-104
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    • 2007
  • The expansion behavior of polystyrene (PS) chains with various molecular weights has been investigated above Flory $\Theta$temperature by viscometry after dissolving in the three different mixed solvents systems such as benzene/n-heptane, 1,4-dioxane/isopropanol, and 1,4-dioxane/n-heptane. Two different regimes are observed as increasing temperature: one regime is for the expansion of chain and the other is for the contraction. For the higher molecular weight sample of PS, the higher peak temperature showing its maximum expansion is obtained. Within a certain system of Ps/mixed solvents, the $\tau/\tau_c$ parameter shows universality for the variation of molecular weight. But while each system of Ps/mixed solvents has shown its own different slope, the universality breaks down in the overall system of mixed solvents. However after introducing a new empirical $b^{2/3}\tau/\tau_c$ parameter, all data points of three different systems have dropt on one master curve and the universality of chain expansion has recovered again. Here $\tau$ and $\tau_c$ are defined as $(T-\Theta)/\Theta$ and $(\Theta-T_c)/T_c$, respectively and $T_c$ is the critical solution temperature, and b of Schultz-Flory equation is corresponding to the effective slope in the plot of $1/T_c$ against $1/M_w^{1/2}$.