• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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• pp.581-600
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• 2021

In this paper we obtain a unique common fixed point theorem for four self-maps which are involved in (𝜙, 𝜓)-weak contraction of a partially ordered b-metric space. The necessary condition has been given to a space for the existence of an unique common fixed of the maps. And our work changed conditions and nonlinear contraction, and search for the unique common fixed point of the maps.

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.309-322
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• 2022

In this paper, we introduce the notion of a new generalized type of rational F-contraction mapping. Further, the concept is used to obtain fixed points in a complete b-metric space. We also prove another unique fixed point theorem in the context of b-metric space. Our results are verified with example.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1147-1170
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• 2022

In this paper, we introduce a new class of mappings called the generalized orthogonal F-Suzuki contraction for a family of multivalued mappings in the setup of orthogonal b-metric spaces. We established the existence of some common fixed point results without using any commutativity condition for this new class of mappings in orthogonal b-metric spaces. Moreover, we illustrate and support these common fixed point results with example. The results obtained in this work generalize and extend some recent and classical related results in the existing literature.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.2
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• pp.221-228
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• 1998

In order to look into the comparative flow characteristics between a circular contraction duct and a circular expansion duct the both centerline turbulent structures have been investigated by the hot wire anemometry. Both of the contraction and the expansion have Morel type contours. Means, turbulences, and triple moments have been measured for the turbulent kinetic energy budgets along their centerlines. It is resulted that mean velocities of both have much deviated from theoretical values calculated by one-dimensional continuity considerations, and that for the same upstream condition, the expansion maintains the isotropy in general while the contraction maintains a severe anisotropy through the whole duct. The mean transport of the TKE along the expansion is willing to balance mostly with the dissipation in the TKE budgets while that along the contraction is balanced with the production in the turbulent kinetic energy equation.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1107-1121
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• 2020

The purpose of this paper is to introduce the notion of generalized multivalued Ƶ-contraction and generalized multivalued Suzuki type Ƶ-contraction for pair of mappings and establish common fixed point theorems for such mappings in complete metric spaces. Results obtained in this paper extend and generalize some well known fixed point results of the literature. We deduce some corollaries from our main result and provide examples in support of our results.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.65-74
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• 2017

In this paper, we establish a unique common fixed point theorem for T-contraction of two self maps on generalized cone b-metric spaces with solid cone. The result of this paper improves and generalizes several well-known results in the literature. Two examples are also given to support the result.

• Nonlinear Functional Analysis and Applications
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• v.26 no.4
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• pp.685-700
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• 2021

In this paper, we discuss the existence and uniqueness of fixed point and common fixed point theorems in complex valued extended b-metric spaces for a pair of mappings satisfying some rational contraction conditions which generalized and unify some well-known results in the literature.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.289-301
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• 2021

In this research, we interpret the notion of a b-cyclic (𝚽, C, D)-contraction for the pair (g, S) of self-mappings on the set Y. We employ our definition to introduce some common fixed point theorems for the two mappings g and S under a set of conditions. Also we introduce an example to support our results.

• YAKHAK HOEJI
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• v.36 no.5
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• pp.496-505
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• 1992

The correlation between GABA receptors($GABA_A$ and $GABA_B$ receptor) and benzodiazepine receptor on the saline infusion-induced micturition reflex contraction was studied in the female rat. To investigate the effect of ${\gamma}-aminobutyric$ acid(GABA) on the micturition reflex, exogenous GABA(10 mg/kg) and GABA transaminase inhibitor(aminooxyacetic acid; AOAA $1\;{\mu}g$) were administered intravenously(i.v.) and intracerebroventriculary(i.c.v.), respectively. In result, both GABA and AOAA inhibited the saline induced micturition reflex contraction. This AOAA induced inhibition of micturition reflex was blocked by both bicuculine. $GABA_A$ receptor antagonist, and Ro 15-1788, benzodiazepine receptor antagonist. Muscimol, $GABA_A$ receptor antagonist($0.1\;{\mu}g$ i.c.v., $3\;{\mu}g$ intrathecal; i.t., 1 mg/kg i.v.) and baclofen, $GABA_A$ receptor agonist($1\;{\mu}g$ i.c.v., $3\;{\mu}g$ i.t., 1 mg/kg i.v.) also inhibited the bladder contraction. Pretreatment of bicuculline($1\;{\mu}g$ i.c.v.), but not of 5-aminovaleric acid(AVA, $1\;{\mu}g$ i.c.v.), $GABA_B$ receptor antagonist blocked the central inhibition of muscimol. These inhibitory effects were reversed by Ro15-1788 but were potentiated by flurazepam, benzodiazepine receptor antagonist. On the other hand, the inhibitory effects of baclofen were not affected by Ro 15-1788. Diazepam and flurazepam also inhibited the micturition reflex contraction when they were administered $3\;{\mu}g$ i.c.v., $10\;{\mu}g$ i.t., $10\;{\mu}M$, $30\;{\mu}M$ transurethrally, respectively. In conclusion, these results suggest that the micturition reflex is mediated by $GABA_A$, $GABA_B$ receptor and benzodiazepine receptor. The bezodiazepines increase the receptor binding of GABA to the $GABA_A$ receptor, so that the benzodiiazepines show the synergistic effect on the inhibition of the micturition reflex contraction, but not to the $GABA_B$ receptor.

• Journal of the Korean Mathematical Society
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• v.40 no.6
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• pp.933-942
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• 2003

It is shown that if a paranormal contraction T has no nontrivial invariant subspace, then it is a proper contraction. Moreover, the nonnegative operator Q = T/sup 2*/T/sup 2/ - 2T/sup */T ＋ I also is a proper contraction. If a quasihyponormal contraction has no nontrivial invariant subspace then, in addition, its defect operator D is a proper contraction and its itself-commutator is a trace-class strict contraction. Furthermore, if one of Q or D is compact, then so is the other, and Q and D are strict ontraction.