• 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.

• Journal of the Korean Home Economics Association
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• v.20 no.4
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• pp.1-12
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• 1982

This study was to investigate the changes of shape of the lower limb surface, the rate of the measurement of expansion and contraction and correlation coefficient between variables caused by hip joint and knee joint movements. The results of the investigation are as follows; 1. According to the development figure of shell when the leg was raised $45^{\circ}$forward($M_{2}$), total length of F.L shortened while B.L lengthened. This result is contarary to $M_{3}$raising the leg $15^{\circ}$ backward. In both $M_{2}$, $M_{3}$movements, the rate of expansion and contraction to the course direction was insignificant. When hip joint was bent $15^{\circ}$ with knee joint $120^{\circ}$bent ($M_{4}$) and hip joint was bent $30^{\circ}$ with knee joint $90^{\circ}$ bent($M_{5}$), upper section of back hip expanded while the front hip section contracted slightly. In the Movement of sitting on the chair($M_{6}$), abdomen, front hip section and upper thight section contracted to the wale direction remarkably while the back hip section expanded conspicuously. 2. According to the rate of expansion and contraction of skin (surface) by the somatometry. In $M_{2}$, C.F.L. upper and middle thight girth contracted and B.L, C.L, L.L expanded. This fact is contarary to M3. In M4, M5, C.F.L showed remarkable contraction and C.B.L expanded remarkably. In $M_{6}$, C.B.L contracted most of all the items measured and knee girth, F.L, L.L, C.B.L, hip girth expanded conspicuously. 3. According to the correlation coefficient between variables. In various movements, the correlation among girth items commonly showed a high or middle grade, the correlation among length items also commonly showed a low grade and that girth and length items showed a very low grade commonly. Waist girth, hip grith, F.L, B.L, L.L items showed that there were significant correlation.

• The Pure and Applied Mathematics
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• v.27 no.4
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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.

• The Pure and Applied Mathematics
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• v.26 no.4
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• pp.277-288
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• 2019

The main objective of this article is to establish some coincidence point theorem for g-non-decreasing mappings under contraction mapping principle on a partially ordered metric space. Furthermore, we constitute multidimensional results as a simple consequences of our unidimensional coincidence point theorem. Our results improve and generalize various known results.

• The Pure and Applied Mathematics
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• v.26 no.4
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• pp.289-303
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• 2019

We study the existence and uniqueness of fixed point for isotone mappings of any number of arguments under Mizoguchi-Takahashi contraction on a complete metric space endowed with a partial order. As an application of our result we study the existence and uniqueness of the solution to integral equation. The results we obtain generalize, extend and unify several very recent related results in the literature.

• The Pure and Applied Mathematics
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• v.17 no.2
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• pp.157-165
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• 2010

Let (M,p) be a germ of a $C^{\infty}$ CR manifold of CR dimension n and CR codimension d. Suppose (M,p) admits a $C^{\infty}$ contraction at p. In this paper, we show that (M,p) is CR equivalent to a generic submanifold in $\mathbb{C}^{n+d}$ defined by a vector valued weighted homogeneous polynomial.

• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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• pp.169-177
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• 2005

A Hilbert Space operator T is of class Q if $T^2{\ast}T^2-2T{\ast}T + I$ is nonnegative. Every paranormal operator is of class Q, but class-Q operators are not necessarily normaloid. It is shown that if a class-Q contraction T has no nontrivial invariant subspace, then it is a proper contraction. Moreover, the nonnegative operator Q = $T^2{\ast}T^2-2T{\ast}T + I$ also is a proper contraction.

• The Pure and Applied Mathematics
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• v.27 no.3
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• pp.109-124
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• 2020

We establish coincidence point theorem for S-non-decreasing mappings under Geraghty-type contraction on partially ordered metric spaces. With the help of obtain result, we derive two dimensional results for generalized compatible pair of mappings F, G : X² → X. As an application, we obtain the solution of integral equation and also give an example to show the usefulness of our results. Our results improve, sharpen, enrich and generalize various known results.

• The Pure and Applied Mathematics
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• v.30 no.3
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• pp.249-267
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• 2023

This manuscript is divided into three segments. In the first segment, we prove a unique common fixed point theorem satisfying generalized weak contraction on partially ordered metric spaces and also give an example to support our results presented here. In the second segment of the article, some common coupled fixed point results are derived from our main results. In the last segment, we investigate the solution of integral equation as an application. Our results generalize, extend and improve several well-known results of the existing literature.

• The Pure and Applied Mathematics
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• v.30 no.3
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• pp.289-307
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• 2023

We prove some common fixed point theorems for β-non-decreasing mappings under contraction mapping principle on partially ordered metric spaces. We study the existence of solution for periodic boundary value problems and also give an example to show the degree of validity of our hypothesis. Our results improve and generalize various known results.