• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.27 no.3
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• pp.160-179
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• 2023

In this paper, we investigate the existence and diameter of the approximate fixed point results on E-metric spaces (not necessarily complete) by using various cyclic contraction mappings, including the B-cyclic contraction, the Bianchini cyclic contraction, the Hardy-Rogers cyclic contraction, and so on. Additionally, we prove the approximate fixed point results for rational type cyclic contraction mappings, which were discussed mainly in [35] and [37], in the setting of E-metric space. Also, a few examples are provided to demonstrate our findings. Subsequently, we discuss some applications of approximate fixed point results in the field of applied mathematics rigorously.

• The Korean Journal of Physiology
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• v.29 no.1
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• pp.39-50
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• 1995

This study was designed to clarify the action of cyclic nucleotides, cyclic AMP and cyclic GMP, on phorbol 12,13-dibutyrate (PDBu)-induced contraction in rings isolated from rabbit carotid artery. Arterial rings, 2 mm in width, were myographied isometrically in an isolated organ bath. PDBu produced slowly developing, sustained contraction in rabbit carotid artery, in a dose dependent manner, which was independent of extracellular $Ca^{2+}$ PDBu-induced contraction was relaxed by staurosporine, which suggests that PDBu-induced contraction is mediated by protein kinase C (PKC). $^{45}Ca^{2+}$ uptake by rabbit carotid artery was increased by PDBu during depolarization, but not in control. Isoproterenol and sodium nitroprusside (SNP) relaxed phenylephrine-induced contraction. However, SNP but not isoproterenol relaxed the contraction induced by PDBu. Acetylcholine relaxed PDBu-induced contraction in the presence of the endothelium. 8-bromo-cyclic AMP, a permeable analogue of cyclic AMP, suppressed phenylephrine-induced contraction but not PDBu-induced contraction. 8-bromo cyclic GMP relaxed both of them with dose dependency. A large dose of forskolin relaxed PDBu-induced contraction. PDBu increased cyclic AMP without considerable change in the level of cyclic GMP. Based on these findings, PDBu-induced contraction of rabbit carotid artery was relaxed by cyclic GMP more effectively than cyclic AMP, and the action of cyclic AMP could be mediated by cyclic GMP dependent protein kinase. Therefore it is suggested that the antagonistic action between protein kinase C and cyclic GMP-dependent protein kinase plays a major role in the regulation of vascular tone.

• The Pure and Applied Mathematics
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• v.30 no.4
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• pp.417-427
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• 2023

The purpose of this paper is establish the existence of proximity point for the cyclic B-contraction mapping on metric spaces and uniformly convex Banach spaces. Also, we prove the common proximity point for the S-weakly cyclic B-contraction mapping. In addition, a few examples are provided to demonstrate our findings.

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.261-269
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• 2022

The purpose of this paper is to introduce a new generalization class of cyclic mappings, called cyclic generalized 𝜑-weak contraction and obtain a corresponding best proximity point theorem for this cyclic mapping under certain conditions.

• The Pure and Applied Mathematics
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• v.29 no.4
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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.

• The Korean Journal of Physiology and Pharmacology
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• v.3 no.3
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• pp.275-282
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• 1999

Muscle strips and muscle cells from cat stomach were used to investigate whether spontaneously formed cyclic nucleotides were involved in the inhibition of gastric smooth muscle contraction. A phosphodiesterase inhibitor, 3-isobutyl-1-methylxanthine (IBMX), increased the levels of both cyclic GMP (cGMP) and cyclic AMP (cAMP) in resting state cells, while decreasing acetylcholine-induced muscle contraction. Under the influence of IBMX, SQ22536, an adenylyl cyclase inhibitor and methylene blue, a guanylyl cyclase inhibitor completely blocked increases in cAMP and cGMP respectively, without any effect on contraction. However, the combination of SQ22536 and methylene blue completely blocked increases in both cAMP and cGMP levels and stimulated contractions markedly even in the presence of IBMX. Muscle contraction inhibitors such as isoprenaline, vasoactive intestinal polypeptide and sodium nitroprusside also appeared to increase cyclic nucleotide levels which decreased contraction. Which nucleotide increased the most was dependent on the agonist used. Therefore, irrespective of the cyclic nucleotide class, the spontaneous formation of cyclic nucleotides should be considered in evaluating the mechanism of gastric smooth muscle relaxation.

• Journal of Korean Institute of Industrial Engineers
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• v.19 no.4
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• pp.87-96
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• 1993

Spectrum analysis of surface electromyogram (FMG) signals is an effective approach to the study of localized muscular fatigue during isometric contraction. Many investigators have con firmed the frequency of the EMG signals being lowered during sustained contaction. In this study, the cyclic loading tasks were performed, and a comparison was made for the median power frequency shift pattern of the EMG signals with the sustained contraction of the same load. The median power frequency shift of the EMG signals for the cyclic loading task was found to be a part of that for the sustained contraction. Based on this result, a new muscle fatigue index was computed by normalizing the duration of the sustained contraction. A fatigue index was obtained as a function of exertion level and the work/rest schedule. With the proposed fatigue index, it is possible to evaluate or predict the degree of muscular fatigue for a physically demanding task.

• The Korean Journal of Pharmacology
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• v.31 no.3
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• pp.285-290
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• 1995

This study was undertaken to define the varying responses of vascular smooth muscle to different wavelengths of ultraviolet radiation and to relate them to the changes in cyclic GMP contents. The ring preparations of rat thoracic aorta with intact or removed endothelium were irradiated with the ultraviolet or visible light (UVR) of wavelengths in step of 10 nm between 250 and 500 nm from xenon lamp of a spectrofluorometer, and the changes in vascular tension were recorded. For cyclic GMP assay, the preparations, pretreated with phenylephrine as in the tension experinents, were frozen after irradiation and homogenated in trichloroacetic acid. The supernatant was extracted with ether and the cyclic GMP contents were measured with radioimmunoassay. In the endothelium-intact preparations, biphasic responses, vasoconstriction (UVR-contraction) followed by vasodilatation (UVR-dilatation), were observed. The maximal UVR-contraction was observed at 320 nm, while the maximal vasodilatation was elicited at 420 nm. In the endothelium-removed rings, however, only vasodilatation was observed, with the maximal vasodilatation taking place at 370 nm. The cyclic GMP contents were not affected by the Irradiation with 320 nm for 30 sec or 1 min in the endothelium-intact preparations, while it was significantly increased by 380 and 420 nm. In the endothelium-removed preparations, UVR of 370 nm markedly increased the cyclic GMP contents. The present study indicates that the increase in cyclic GMP is closely related to vasodilatation induced by UVR of 420 nm in the endothelium-intact or 370 nm in the denuded preparations, whereas it is not involved in the vasoconstriction induced by UVR of 320 nm in the intact rings, and the mechanism leading to UVR-contraction remains to be clarified. These observations suggest that nitric oxide-cyclic GMP system is closely related to the UVR-dilatation in rat aortic preparation, while it is not involved in the UVR contraction.

• Korean Journal of Mathematics
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• v.31 no.2
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• pp.123-131
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• 2023

In this paper, we prove existence of best proximity points for 2-convex contraction, 2-sided contraction, and M-weakly cyclic 2-convex contraction mappings in the setting of complete strongly regular generalized modular metric spaces that generalize many results in the literature.

• The Korean Journal of Physiology and Pharmacology
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• v.13 no.6
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• pp.503-510
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• 2009

To elucidate the mechanism of cyclic nucleotides, such as adenosine 3',5'-cyclic monophosphate (cAMP) and guanosine 3',5'-cyclic monophosphate (cGMP), in the regulation of human gastric motility, we examined the effects of forskolin (FSK), isoproterenol (ISO) and sodium nitroprusside (SNP) on the spontaneous, high $K^+$ and acetylcholine (ACh)-induced contractions of corporal circular smooth muscle in human stomach. Gastric circular smooth muscle showed regular spontaneous contraction, and FSK, ISO and SNP inhibited its phasic contraction and basal tone in a concentration-dependent manner. High $K^+$ (50 mM) produced sustained tonic contraction, and ACh $(10\;{\mu}M)$ produced initial transient contraction followed by later sustained tonic contraction with superimposed phasic contractions. FSK, ISO and SNP inhibited high $K^+$-induced tonic contraction and also ACh-induced phasic and tonic contraction in a reversible manner. Nifedipine $(1\;{\mu}M)$, inhibitor of voltage-dependent L-type calcium current $(VDCC_L)$, almost abolished ACh-induced phasic contractions. These findings suggest that FSK, ISO and SNP, which are known cyclic nucleotide stimulators, inhibit smooth muscle contraction in human stomach partly via inhibition of $VDCC_L$.