• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1087-1094
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• 2016

On a compact n-dimensional manifold M, it has been conjectured that a critical point of the total scalar curvature, restricted to the space of metrics with constant scalar curvature of unit volume, is Einstein. In this paper, after derivng an interesting curvature identity, we show that the conjecture is true in dimension three and four when g is weakly Einstein. In higher dimensional case $n{\geq}5$, we also show that the conjecture is true under an additional Ricci curvature bound. Moreover, we prove that the manifold is isometric to a standard n-sphere when it is n-dimensional weakly Einstein and the kernel of the linearized scalar curvature operator is nontrivial.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.859-870
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• 2015

The notion of quasi-valuation maps based on a subalgebra and an ideal in BCK/BCI-algebras is introduced, and then several properties are investigated. Relations between a quasi-valuation map based on a subalgebra and a quasi-valuation map based on an ideal is established. In a BCI-algebra, a condition for a quasi-valuation map based on an ideal to be a quasi-valuation map based on a subalgebra is provided, and conditions for a real-valued function on a BCK/BCI-algebra to be a quasi-valuation map based on an ideal are discussed. Using the notion of a quasi-valuation map based on an ideal, (pseudo) metric spaces are constructed, and we show that the binary operation * in BCK-algebras is uniformly continuous.

• The Pure and Applied Mathematics
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• v.24 no.2
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• pp.79-98
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• 2017

We establish a coupled coincidence point theorem for generalized compatible pair of mappings $F,G:X{\times}X{\rightarrow}X$ under generalized symmetric Meir-Keeler contraction on a partially ordered metric space. We also deduce certain coupled fixed point results without mixed monotone property of $F:X{\times}X{\rightarrow}X$. An example supporting to our result has also been cited. As an application the solution of integral equations are obtain here to illustrate the usability of the obtained results. We improve, extend and generalize several known results.

• East Asian mathematical journal
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• v.32 no.3
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• pp.333-354
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• 2016

We present coincidence point theorem for g-non-decreasing mappings satisfying generalized nonlinear contraction on partially ordered metric spaces. We show how multidimensional results can be seen as simple consequences of our unidimensional coincidence point theorem. We also obtain the coupled coincidence point theorem for generalized compatible pair of mappings $F,G:X^2{\rightarrow}X$ by using obtained coincidence point results. Furthermore, an example and an application to integral equation are also given to show the usability of obtained results. Our results generalize, modify, improve and sharpen several well-known results.

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.507-518
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• 2020

In this article, we establish some fixed point results in G-metric spaces using the modified JS-G-contractions and we provide some suitable examples to support the results. Also, we give an application to solve an integral equation.

• Journal of the Korean Mathematical Society
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• v.57 no.4
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• pp.935-955
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• 2020

In this paper we present a measurable version of the Smale's spectral decomposition theorem for homeomorphisms on compact metric spaces. More precisely, we prove that if a homeomorphism f on a compact metric space X is invariantly measure expanding on its chain recurrent set CR(f) and has the eventually shadowing property on CR(f), then f has the spectral decomposition. Moreover we show that f is invariantly measure expanding on X if and only if its restriction on CR(f) is invariantly measure expanding. Using this, we characterize the measure expanding diffeomorphisms on compact smooth manifolds via the notion of Ω-stability.

• Bulletin of the Korean Mathematical Society
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• v.45 no.3
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• pp.573-585
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• 2008

A few sufficient conditions for the existence and uniqueness of fixed point and common fixed point for certain contractive type mappings in complete metric spaces are provided. Several existence and uniqueness results of solution and common solution for some functional equations and system of functional equations in dynamic programming are discussed by using the fixed point and common fixed point theorems presented in this paper.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.49 no.8
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• pp.491-494
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• 2000

A scheme is proposed for measuring similarities between the binary pulse signals in the pulse-code modulation using the Integra-Normalizer. The Integra-Normalizer provides a better interpretation of the relationship between the pulse signals by removing redundant codes, which maps all possible observed signals to one of the codes to be received with relative similarities between each pair of compared signals. The proposed method provides better error tolerance than L2 metric, such as Hamming distance, since the distances between pulse signals are measured not useful for the time-delay detection in the pulse-code modulation.

• Textile Coloration and Finishing
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• v.9 no.6
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• pp.51-57
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• 1997

The lightness, chroma and hue tolerances with respect to the standard colour position in the CIELAB space have been studied in detail using the various existing data sets and the set form this study. The lightness tolerance showed a clear dependency upon the metric lightness for medium to light colour, but in the case of dark colours there was a discrepancy between the data sets. Both the chroma and hue tolerances showed dependency upon both the chroma and hue-angle and not the single dependency upon the metric chroma, as assumed in the CIE94 formula. New weighting functions were derived from the above experimental evidence, and finally a new formula, LCD(Leeds Colour Difference) was proposed. The LCD formula is nearly as simple and flexible as CIE94 but smoothes the individual weighting functions, especially for lightness tolerances for light colours and chromaticity discrimination near the blue region.

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.355-361
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• 2006

We prove that if a continuous surjective map f on a compact metric space X has the average shadowing property, then every point x is chain recurrent. We also show that if a homeomorphism f has more than two fixed points on $S^1$, then f does not satisfy the average shadowing property. Moreover, we construct a homeomorphism on a circle which satisfies the shadowing property but not the average shadowing property. This shows that the converse of the theorem 1.1 in [6] is not true.