• 대한수학회보
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• 제45권3호
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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.

• 대한전기학회논문지:시스템및제어부문D
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• 제49권8호
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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.

• 한국염색가공학회지
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• 제9권6호
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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.

• 대한수학회논문집
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• 제21권2호
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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.

• 대한수학회논문집
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• 제34권4호
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• pp.1201-1222
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• 2019

In this paper, we introduce the notion of modified TAC-Suzuki-Berinde type F-contraction and modified TAC-(${\psi}$, ${\phi}$)-Suzuki type rational mappings in the frame work of complete metric spaces, we also establish some fixed point results regarding this class of mappings and we present some examples to support our main results. The results obtained in this work extend and generalize the results of Dutta et al. [9], Rhoades [18], Doric, [8], Khan et al. [13], Wardowski [25], Piri et al. [17], Sing et al. [23] and many more results in this direction.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제28권4호
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• pp.297-314
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• 2021

This manuscript is divided into three segments. In the first segment, we formulate a unique common fixed point theorem satisfying generalized Meir-Keeler contraction on partially ordered metric spaces and also give an example to demonstrate the usability of our result. 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 some periodic boundary value problems. Our results generalize, extend and improve several well-known results of the existing literature.

• 대한수학회보
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• 제60권1호
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• pp.33-46
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• 2023

Geodesic orbit spaces are homogeneous Finsler spaces whose geodesics are all orbits of one-parameter subgroups of isometries. Such Finsler spaces have vanishing S-curvature and hold the Bishop-Gromov volume comparison theorem. In this paper, we obtain a complete description of invariant (α₁, α₂)-metrics on spheres with vanishing S-curvature. Also, we give a description of invariant geodesic orbit (α₁, α₂)-metrics on spheres. We mainly show that a Sp(n + 1)-invariant (α₁, α2)-metric on S⁴ⁿ⁺³ = Sp(n + 1)/Sp(n) is geodesic orbit with respect to Sp(n + 1) if and only if it is Sp(n + 1)Sp(1)-invariant. As an interesting consequence, we find infinitely many Finsler spheres with vanishing S-curvature which are not geodesic orbit spaces.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제31권1호
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• pp.83-102
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• 2024

In this paper, first we establish a unique common fixed point theorem satisfying new contractive condition on partially ordered non-Archimedean fuzzy metric spaces and give an example to support our result. By using the result established in the first section of the manuscript, we formulate a unique common coupled fixed point theorem and also give an example to validate our result. In the end, we study the existence of solution of integral equation to verify our hypothesis. These results generalize, improve and fuzzify several well-known results in the existing literature.

• 대한수학회보
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• 제41권3호
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• pp.457-464
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• 2004

Let X be a Banach space and Z a closed subspace of a Banach space Y. Denote by Ｌ(X, Y) the space of all bounded linear operators from X to Y and by Ｋ(X, Y) its subspace of compact linear operators. Using Hahn-Banach extension operators corresponding to ideal projections, we prove that if either $X^{**}$ or $Y^{*}$ has the Radon-Nikodym property and Ｋ(X, Y) is an M-ideal (resp. an HB-subspace) in Ｌ(X, Y), then Ｋ(X, Z) is also an M-ideal (resp. HB-subspace) in Ｌ(X, Z). If Ｌ(X, Y) has property SU instead of being an M-ideal in Ｌ(X, Y) in the above, then Ｋ(X, Z) also has property SU in Ｌ(X, Z). If X is a Banach space such that $X^{*}$ has the metric compact approximation property with adjoint operators, then M-ideal (resp. HB-subspace) property of Ｋ(X, Y) in Ｌ(X, Y) is inherited to Ｋ(X, Z) in Ｌ(X, Z).

• 호남수학학술지
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• 제31권2호
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• pp.185-201
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• 2009

Let M be a real hypersurface with almost contact metric structure $({\phi},{\xi},{\eta},g)$ of a nonflat complex space form whose structure Jacobi operator $R_{\xi}=R({\cdot},{\xi}){\xi}$ is ${\xi}$-parallel. In this paper, we prove that the condition ${\nabla}_{\xi}R_{\xi}=0$ characterize the homogeneous real hypersurfaces of type A in a complex projective space $P_n{\mathbb{C}}$ or a complex hyperbolic space $H_n{\mathbb{C}}$ when $g({\nabla}_{\xi}{\xi},{\nabla}_{\xi}{\xi})$ is constant.