• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.461-475
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• 2024

The concept of an extension α-F-contraction and it's modified counterpart represents an advancement in the theory of metric space contractions. Through our study of the contraction principles and it's relationship to extension and modified extension, we found different conditions somewhat lengthy. In our paper, we create a development of the conditions for the extension of α-F-contraction and a modified α-F-contraction by reducing the conditions and make them easier. Our propose conditions are notably simple and effective. They serve as the foundation for proving theorems and solving examples that belong to our study. Moreover, they have remarkable significance in the condition of mathematical analysis and problem-solving. Thus, we find that these new conditions that we mention in the definitions achieve what is require and through them, we choose λ = 1 and we choose λ ∈ (0, 1) to clarify our ideas.

• Journal of the Korean Home Economics Association
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• v.26 no.2
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• pp.1-13
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• 1988

The purpose of this study was to classify somatotype of males, to show changes of the body skin surface by the somatotype. The size of sample was 156 males between age 20 and 24. Somatotype classified into Bending somatotype, Standard somatotype, Turning over somatotype. And according to the somatotype, changing of the upper part of the body by the arm movements analyzed through gypsum experiment. The result obtained from this study were as follows; 1. the variation of the upper part of the body form by changing the am movements, by the increasing of movements, shoulder-point ws moved to be inside or upside, the anterior armpit point & armpit point were moved to the upside. 2. As a result of investigating into the rate of the expansion and contraction of the basic lines and body surface area by the arm movements, the rate of expansion and contraction of the basic lines by the arm movements, the side sea length showed the maximum rate of extension in 135 degrees, the shoulder length showed the maximum rate of contraction in 135 degrees. The rate of expansion and contraction on the body surface area by the arm movements showed the phenomenon of contraction, of items F1, F6, B1, B9 showed the phenomenon of extension, of items F3, F4, F8, F9, B8, B9. 3. According to somatotypes, items which show the significant difference were, of items f3, f8, b3, b8, F2, F7, F8, B3, B7, in all movements.

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.581-596
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• 2024

A new variety of non-self generalized proximal contraction, called Hardy-Rogers α⁺F-proximal contraction, is shown in this work. Also, with an example, we prove that such contractions satisfying some conditions must have a unique best proximity point. For some particular values of the constants, that we have used to generalize the proximal contraction, we conclude different α⁺F-proximal contraction results of the types Ćirić, Chatterjea, Reich, Kannan, and Banach with proof, that all such type of contractions must have unique best proximity point. We also apply our result to solve a functional equation.

• Korean Journal of Human Ecology
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• v.7 no.3
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• pp.35-48
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• 2004

In this study, by determining lower limb movements which cause significant changes in body surface lines, body parts with the greatest maximum expansion and contraction rate respectively were illustrated in descending order. Using unmarried female university students aged 18 - 24 as subjects, a total of 32 body surface categories (15 body surface lines and 17 body surface segment lines) were measured in one static and 9 movement poses. In particular, expansion and contraction levels and rates were measured and used in the analysis. The analysis first involved the calculation of the average measurement per body part in body surface line in static pose as well as of the average expansion and contraction levels and rates in 9 lower limb movements. Two-way MANOVA and multiple comparison analysis (Tukey) were conducted on movements and individual somatotypes regarding measurement per body part and expansion and contraction rates. Movements which cause measurements of body surface lines differed significantly in body surface line in static pose versus in movement were then identified. Among average expansion and contraction rates in such movements, maximum average expansion and contraction levels, maximum average expansion and contraction rate, and classes of expansion and contraction rate were determined per body part. The results of this study are as follows. First, 5 lower limb movements; F2, F5, F6, F7, F8, which caused significant changes in body surface lines were determined and illustrated in table 4. Second, the levels, rates, and classes of expansion and contraction rate per body part are illustrated in Tables 5 and 6. Body parts with the greatest maximum expansion rate were, in descending order: upper segment of center back leg line, upper segment of inner leg line, middle segment of center front leg line, posterior crotch length, anterior knee girth, anterior thigh girth, center back leg line, girth at crotch height, anterior midway thigh girth, hip girth, anterior crotch length, knee girth, waist girth, inner leg line, thigh girth, and crotch length. Those with the greatest maximum contraction rate were, in descending order: anterior crotch length, upper segment of center front leg line, lower segment of center back leg line, center front leg line, and posterior thigh girth. The maximum expansion rates and maximum contraction rates, which ranged from 2.05 to $35.95\%$ and from -0.20 to $-30.16\%$ respectively, were classified per body part into 4 ABCD classes. The body part with maximum expansion was the upper segment of the center back leg line at vertical body surface line, expanding by $35.95\%$ or 16.03cm in F5 flexion movement. In contrast, the body part with maximum contraction was the anterior crotch length at vertical body surface line, contracting by $-30.16\%$ or -10.54cm in F5 flexion movement. Both, however, were the body parts to expand or contract the most among all horizontal and vertical body surface lines.

• The Korean Journal of Pharmacology
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• v.23 no.2
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• pp.133-141
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• 1987

The effects of verapamil and tetracaine on acetylcholine-and oxytocin-induced contraction of uterus from estrogen-treated rat were examined. Isometric tensions were recorded on the Physiograph and stored in TriGem 20XT computer as digitized data for off-line analysis of the components, which described the contraction patterns: trought tension (T), peak tension (P), contraction frequency (F), and duration (D). In the acetylcholine-induced contraction, verapamil $(0.25\;{\mu}M)$ significantly decreased P and D. In contrast, tetracaine $(42{\mu}M)$ decreased F, but increased D. In the low oxytocin-induced contraction, verapamil $(0.25\;{\mu}M)$ decreased P and D, and tetracaine $(42{\mu}M)$ decreased F but increased D. In the high oxytocin-induced contraction, verapamil decreased P and D, but tetracaine decreased P without affecting on other components. These results suggest that the analysis of effects of a certain inhibitor on the components of contraction allow to postulate its specific inhibitory mechanism of the smooth muscle contraction.

• Korean Journal of Mathematics
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• v.31 no.4
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• pp.391-403
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• 2023

In this work, we establish common fixed point results by utilizing a variant of F-contraction in the framework of C^*-algebra valued metric spaces. We utilize E.A. and C.L.R. property possessed by the mappings to prove common fixed point results in the same metric settings. To validate the applicability of these common fixed point results, we provide illustrative examples too.

• The Pure and Applied Mathematics
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• v.31 no.1
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• pp.103-117
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• 2024

In this article, we utilize the concepts of hybrid rational Geraghty type generalized F-contraction and to prove some fixed point results for such mappings are in the perspective of partially ordered b-metric like space. Some innovative examples are also presented which substantiate the validity of obtained results. The example is also authenticated with the help of graphical representations.

• 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.

• The Korean Journal of Physiology
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• v.24 no.2
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• pp.353-362
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• 1990

Fluoride (F-), a known stimulator of G-protein, induced strong contraction in rabbit trachealis muscle. $AlCl_3\;(5{\sim}20\;{\mu}M)$, which is required for G-protein stimulation by $F^-$, potentiated the contractile response to $F^-$. $Ca^{2+}-removal$ and verapamil, a calcium channel blocker, inhibited the fluoroaluminate-induced contraction. Fluoroaluminate increased $^{45}Ca$ influx in the absence and presence of verapamil. In heparin-loaded muscle high $K^+-induced$ contraction was not affected, but acetylcholine and fluoroaluminate-induced contractions were inhibited. The fluoroaluminate-induced contraction was partially relaxed by isoproterenol, a stimulator of adenylate cyclase. Pertussis toxin partially inhibited fluoroaluminate-induced contraction and potentiated isoproterenol-induced relaxation in the presence of fluoroaluminate, but had no effect on acetylcholine-induced contraction and the isoproterenol-induced relaxation in the presence of acetylcholine. These results suggest that fluoroaluminate has the ability to stimulate at least two putative G-proteins in rabbit trachealis muscle; One causes $Ca^{2+}$ influx through the potential-operated $Ca^{2+}$ channel and the other induces intracellular $Ca^{2+}$ release by the increase of inositol-1, 4, 5-triphosphate.

• Honam Mathematical Journal
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• v.41 no.1
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• pp.19-34
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• 2019

The article is written with a view to introducing the new idea of an F-contraction on a closed ball and have new ${\acute{C}}iri{\acute{c}}$ type fixed point theorems in the framework of a complete metric space. That is why this outcome becomes useful for the contraction of the mapping on a closed ball instead of the whole space. At the same time, some comparative examples are constructed which establish the superiority of our results. It can be stated that the results that have come into being give proof of extension as well as substantial generalizations and improvements of several well known results in the existing comparable literature.