• 한국수학교육학회지시리즈B:순수및응용수학
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• 제14권4호
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• pp.283-287
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• 2007

An extension of the contraction mapping theorem is provided in a Banach space setting to approximate fixed points of operator equations. Our approach is justified by numerical examples where our results apply whereas the classical contraction mapping principle cannot.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제26권4호
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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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권3호
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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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권4호
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• pp.443-461
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• 2023

In this paper, we establish some common fixed point theorems satisfying contraction mapping principle on partially ordered non-Archimedean fuzzy metric spaces and also derive some coupled fixed point results with the help of established results. We investigate the solution of integral equation and also give an example to show the applicability of our results. These results generalize, improve and fuzzify several well-known results in the recent literature.

• Korean Journal of Mathematics
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• 제26권4호
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• pp.809-822
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• 2018

In this paper, we introduce complex valued dislocated metric spaces. We prove Banach contraction principle, Kannan and Chatterjea type fixed point theorems in this new space. Moreover, we give some applications of the results to differential equations and iterated functions.

• East Asian mathematical journal
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• 제40권1호
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• pp.37-50
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• 2024

We establish the existence, multiplicity and uniqueness of positive solutions to nonlocal boundary value systems with strongly coupled integral boundary condition by using the global continuation theorem and Banach's contraction principle.

• 대순사상논총
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• 제26집
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• pp.77-110
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• 2016

The purpose of this article is to study on the Correlative linkage between the cosmic principle of birth-growth and contraction-recess and the Non action Tao. The split time between birth-growth and contraction-recess is the conflict between the Prior Time and Posterior Time as the Great Renewal. The cycle of this Chaotic Renewals is the cycle of a cosmic circulation as 129,600 years. In relation to the correlative linkage of function, Jeong-san Sangje governs all the beings of the universe by means of the cosmic principle birth-growth and contraction-recess. Also Jeong-san Sangje, using the Non action Tao governing all the beings of the universe and let them exist as the original selves. Thus, the two necessities are mutual interdependent and mutual complementary. In relation to the correlative linkage of substance, Jeong-san Sangje is included in the cosmic life which forms of all the existences. That is personal God of Jeong-san Sangje that is a part of the cosmic life. So that Jeong-san Sangje is included in the cosmic life, the basis of all the cosmic affairs. He is also subordinate to the cosmic principle but he simultaneously governs it. Jeong-san Sangje is trans-versal mediator between the cosmic principle and the cosmic life of Non action Tao, since it is the origin of his mind. To understand the nature of Jeong-san Sangje who becomes one with the cosmic life, the old causal way of thinking which inquires the timely order and seeks for causes and effects should be abandoned. The new way of thinking is thus different from the old one. The core of cosmic life is abstracted as the essence-energy and god-blood. This structure is similar to the cosmic principle of birth-growth and contraction-recess. The death is a kind of event caused by the depletion of the essence, and all beings could altered into the god. It also would be returned to the natural birth place of the cosmos, as it were, that can be called the 'Return to the Origin'. As the cosmos goes to the new epoch, humans have been living together with the cosmic principle. Now we can expect the Posterior Time to open to humans as cosmic life of Non action Tao.

• 호남수학학술지
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• 제30권1호
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• pp.197-203
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• 2008

We show the existence of the unique solution of the following system of the nonlinear wave equations with Dirichlet boundary conditions and periodic conditions under some conditions $U_{tt}-U_{xx}+av^+=s{\phi}_{00}+f$ in $(-{\frac{\pi}{2},{\frac{\pi}{2}}){\times}R$, ${\upsilon}_{tt}-{\upsilon}_{xx}+bu^+=t{\phi}_{00}+g$ in $(-{\frac{\pi}{2},{\frac{\pi}{2}}){\times}R$, where $u^+$ = max{u, 0}, s, t ${\in}$ R, ${\phi}_{00}$ is the eigenfunction corresponding to the positive eigenvalue ${\lambda}_{00}$ of the wave operator. We first show that the system has a positive solution or a negative solution depending on the sand t, and then prove the uniqueness theorem by the contraction mapping principle on the Banach space.

• Nonlinear Functional Analysis and Applications
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• 제28권2호
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• pp.311-335
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• 2023

Fixed point theory is the center of focus for many mathematicians from last few decades. A lot of generalizations of the Banach contraction principle have been established. In this paper, we introduce the concepts of 𝜃-contraction and 𝜃-𝜑-contraction in quasi-metric spaces to study the existence of the fixed point for them.

• Korean Journal of Mathematics
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• 제16권4호
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• pp.545-551
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• 2008

We investigate the multiple solutions for a parabolic boundary value problem with jumping nonlinearity crossing no eigenvalues. We show the existence of the unique solution of the parabolic problem with Dirichlet boundary condition and periodic condition when jumping nonlinearity does not cross eigenvalues of the Laplace operator $-{\Delta}$. We prove this result by investigating the Lipschitz constant of the inverse compact operator of $D_t-{\Delta}$ and applying the contraction mapping principle.