• 호남수학학술지
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• 제36권1호
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• pp.103-112
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• 2014

There are several theories to say that 'Mathematics is beautiful', but the typical one of them is a theory about the golden ratio. Often the golden ratio apt to be considered only as the geometric shapes or the simple number of ratio used in buildings and arts. However in this paper, we studied to consider the mathematical theories which are contained in their inside. In particular, we investigate the various expressions of the continued fraction which are represented by the golden ratio.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제11권1호
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• pp.25-32
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• 2011

In this paper, we study the existence and uniqueness of solutions for the impulsive semilinear fuzzy integrodifferential equations with nonlocal conditions and forcing term with memory in n-dimensional fuzzy vector space ($E^n_N$, $d_{\varepsilon}$) by using Banach fixed point theorem. That is an extension of the result of Kwun et al. [9] to impulsive system.

• Journal of applied mathematics & informatics
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• 제33권5_6호
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• pp.475-484
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• 2015

In this article, we deal with the uniqueness problems of meromorphic functions concerning differential polynomials and prove the following theorem. Let f and g be two nonconstant meromorphic functions, n ≥ 12 a positive integer. If fⁿ(f³ - 1)f′ and gⁿ(g³ - 1)g′ share (1, 2), f and g share ∞ IM, then f ≡ g. The results in this paper improve and generalize the results given by Meng (C. Meng, Uniqueness theorems for differential polynomials concerning fixed-point, Kyungpook Math. J. 48(2008), 25-35), I. Lahiri and R. Pal (I. Lahiri and R. Pal, Nonlinear differential polynomials sharing 1-points, Bull. Korean Math. Soc. 43(2006), 161-168), Meng (C. Meng, On unicity of meromorphic functions when two differential polynomials share one value, Hiroshima Math.J. 39(2009), 163-179).

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.79-87
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• 2009

This paper deals with the multipoint boundary value problem for one dimensional p-Laplacian $({\phi}_p(u'))'(t)$ + f(t,u(t)) = 0, $t{\in}$ (0, 1), subject to the boundary value conditions: u'(0) - $\sum\limits^n_{i=1}{\alpha_i}u({\xi}_i)$ = 0, u'(1) + $\sum\limits^n_{i=1}{\alpha_i}u({\eta}_i)$ = 0. Using a fixed point theorem for operators on a cone, we provide sufficient conditions for the existence of multiple (at least three) positive solutions to the above boundary value problem.

• 대한수학회보
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• 제52권2호
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• pp.421-438
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• 2015

In this paper, we study the existence of classical and generalized solutions for nonlinear differential inclusions $x^{\prime}(t){\in}F(t,x(t))$ in Hilbert spaces in which the multifunction F on the right-hand side is hemicontinuous and satisfies the semimonotone condition or is condensing. Our existence results are obtained via the selection and fixed point methods by reducing the problem to an ordinary differential equation. We first prove the existence theorem in finite dimensional spaces and then we generalize the results to the infinite dimensional separable Hilbert spaces. Then we apply the results to prove the existence of the mild solution for semilinear evolution inclusions. At last, we give an example to illustrate the results obtained in the paper.

• 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).

• 한국산업융합학회 논문집
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• 제5권3호
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• pp.219-224
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• 2002

We consider the problem y"=a(x,y)(y-b), y(0)=0, y'(1)=g(y(${\xi}$), y'(${\xi}$)), (0${\xi}$ fixed in(0,1)) as a model of steady-slate heat conduction in a rod when the heat flux at the end x = 1 is determined by observation of the temperature and heat flux at some interior point ${\xi}$. We establish conditions sufficient for existence, uniqueness.

• 대한수학회논문집
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• 제35권3호
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• pp.891-906
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• 2020

In this paper, the commutative module amenable Banach algebras are characterized. The hereditary and permanence properties of module amenability and the relations between module amenability of a Banach algebra and its ideals are explored. Analogous to the classical case of amenability, it is shown that the projective tensor product and direct sum of module amenable Banach algebras are again module amenable. By an application of Ryll-Nardzewski fixed point theorem, it is shown that for an inverse semigroup S, every module derivation of 𝑙¹(S) into a reflexive module is inner.

• 대한수학회논문집
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• 제21권4호
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• pp.665-673
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• 2006

In a recent paper, Domokos and $Kolumb\'{a}}n$ [2] gave an interesting interpretation of variational inequalities (VI) and vector variational inequalities (VVI) in Banach space settings in terms of variational inequalities with operator solutions (in short, OVVI). Inspired by their work, in a former paper [4], we proposed the scheme of generalized vector variational inequality with operator solutions (in short, GOVVI) which extends (OVVI) into a multivalued case. In this note, we further develop the previous work [4]. A more general pseudomonotone operator is treated. We present a result on the existence of solutions of (GVVI) under the weak pseudomonotonicity introduced in Yu and Yao [8] within the framework of (GOVVI) by exploiting some techniques on (GOVVI) or (GVVI) in [4].

• 대한수학회지
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• 제45권3호
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• pp.841-858
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• 2008

In this paper, we introduce two classes of generalized variational-like inequalities with compositely monotone multifunctions in Banach spaces. Using the KKM-Fan lemma and the Nadler's result, we prove the existence of solutions for generalized variational-like inequalities with compositely relaxed ${\eta}-{\alpha}$ monotone multifunctions in reflexive Banach spaces. On the other hand we also derive the solvability of generalized variational-like inequalities with compositely relaxed ${\eta}-{\alpha}$ semimonotone multi functions in arbitrary Banach spaces by virtue of the Kakutani-Fan-Glicksberg fixed-point theorem. The results presented in this paper extend and improve some earlier and recent results in the literature.