• 충청수학회지
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• 제28권3호
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• pp.451-463
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• 2015

A continuous and non-decreasing function ${\psi}$ and another continuous function ${\phi}$ with ${\phi}(z)=0{\Leftrightarrow}z=0$ defined on $\mathbb{C}^+=\{x+yi:x,y{\geq}0\}$ are introduced, the ${\psi}-{\phi}$-contractive or expansive type conditions are considered, and the existence theorems of common fixed points for two mappings defined on a complex valued metric space are obtained. Also, Banach contraction principle and a fixed point theorem for a I-expansive type mapping are given on complex valued metric spaces.

• 대한수학회보
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• 제55권3호
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• pp.899-911
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• 2018

In this paper, we consider the second-order nonlinear differential equation with the nonlocal boundary conditions. We first reformulate this boundary value problem as a fixed point problem for a Fredholm integral equation operator, and then present a result on the existence and uniqueness of the solution by using the contraction mapping theorem. Furthermore, we establish a sufficient condition on the functions ${\mu}$ and $h_i$, i = 1, 2 that guarantee a unique solution for this nonlocal problem in a Hilbert space. Also, accurate analytic solutions in series forms for this boundary value problems are obtained by the Adomian decomposition method (ADM).

• 대한수학회보
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• 제54권1호
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• pp.199-214
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• 2017

We consider fixed-point iterations constructed by simple transforming from a quadratic matrix equation to equivalent fixed-point equations and assume that the iterations are well-defined at some solutions. In that case, we suggest real valued functions. These functions provide radii at the solution, which guarantee the local convergence and the uniqueness of the solutions. Moreover, these radii obtained by simple calculations of some constants. We get the constants by arbitrary matrix norm for coefficient matrices and solution. In numerical experiments, the examples show that the functions give suitable boundaries which guarantee the local convergence and the uniqueness of the solutions for the given equations.

• Korean Journal of Mathematics
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• 제16권3호
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• pp.355-362
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• 2008

We prove the existence of a unique positive solution for a class of systems of the following nonlinear suspension bridge equation with Dirichlet boundary conditions and periodic conditions $$\{{u_{tt}+u_{xxxx}+\frac{1}{4}u_{ttxx}+av^+={\phi}_{00}+{\epsilon}_1h_1(x,t)\;\;in\;(-\frac{\pi}{2},\frac{\pi}{2}){\times}R,\\{v_{tt}+v_{xxxx}+\frac{1}{4}u_{ttxx}+bu^+={\phi}_{00}+{\epsilon}_2h_2(x,t)\;\;in\;(-\frac{\pi}{2},\frac{\pi}{2}){\times}R,$$ where $u^+={\max}\{u,0\},\;{\epsilon}_1,\;{\epsilon}_2$ are small number and $h_1(x,t)$, $h_2(x,t)$ are bounded, ${\pi}$-periodic in t and even in x and t and ${\parallel} h_1{\parallel}={\parallel} h_2{\parallel}=1$. We first show that the system has a positive solution, and then prove the uniqueness by the contraction mapping principle on a Banach space

• East Asian mathematical journal
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• 제26권5호
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• pp.671-680
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• 2010

A system of nonlinear variational inclusions involving general H-monotone operators in Banach spaces is introduced. Using the resolvent operator technique, we suggest an iterative algorithm for finding approximate solutions to the system of nonlinear variational inclusions, and establish the existence of solutions and convergence of the iterative algorithm for the system of nonlinear variational inclusions.

• 한국지능시스템학회논문지
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• 제18권4호
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• pp.524-529
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• 2008

Park et.al.[10] defined the intuitionistic fuzzy metric space in which it is a little revised in Park[4], and Park et.a1.[7] proved a fixed point theorem of Banach for the contractive mapping of a complete intuitionistic fuzzy metric space. In this paper, we will establish common fixed point theorem for four self maps in intuitionistic fuzzy metric space. These results have been used to obtain translation and generalization of Grabiec's contraction principle.

• 대한수학회보
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• 제53권2호
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• pp.335-350
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• 2016

Based on the notion of $q_k$-derivative introduced by the authors in [17], we prove in this paper existence and uniqueness results for nonlinear second-order impulsive $q_k$-difference equations with anti-periodic boundary conditions. Two results are obtained by applying Banach's contraction mapping principle and Krasnoselskii's fixed point theorem. Some examples are presented to illustrate the results.

• Kyungpook Mathematical Journal
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• 제59권1호
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• pp.73-82
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• 2019

In this work, we give necessary and sufficient conditions under which every solution of a class of first-order neutral differential equations of the form $$(x(t)+p(t)x({\tau}(t)))^{\prime}+q(t)Hx({\sigma}(t)))=0$$ either oscillates or converges to zero as $t{\rightarrow}{\infty}$ for various ranges of the neutral coefficient p. Our main tools are the Knaster-Tarski fixed point theorem and the Banach's contraction mapping principle.

• 호남수학학술지
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• 제42권4호
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• pp.667-680
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• 2020

Our paper deals with the following neutral nonlinear Levin-Nohel integro-differential with variable delay $${\frac{d}{dt}x(t)}+{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{t-r(t)}}^t}a(t,s)x(s)ds+{\frac{d}{dt}}g(t,x(t-{\tau}(t)))=0.$$ By using Krasnoselskii's fixed point theorem we obtain the existence of periodic and positive periodic solutions and by contraction mapping principle we obtain the existence of a unique periodic solution. An example is given to illustrate this work.

• Kyungpook Mathematical Journal
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• 제63권3호
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• pp.437-450
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• 2023

In this paper, we present a sufficient condition for the unique existence of solutions for a coupled system of nonlinear fractional Langevin equations with a new class of multipoint and nonlocal integral boundary conditions. We define a 𝓩^*_λ-contraction mapping and present the sufficient condition by identifying the problem with an equivalent fixed point problem in the context of b-metric spaces. Finally, some numerical examples are given to validate our main results.