• Journal of the Korean Mathematical Society
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• v.41 no.3
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• pp.567-589
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• 2004

In the present paper, we treat an infinite series ($\alpha$, $\beta$)-metric L =$\beta$$^2$/($\beta$-$\alpha$). First, we find the conditions that a Finsler metric F$^{n}$ with the metric above be a Berwald space, a Douglas space, and a projectively flat Finsler space, respectively. Next, we investigate the condition that a two-dimensional Finsler space with the metric above be a Landsbeg space. Then the differential equations of the geodesics are also discussed.

• Communications of the Korean Mathematical Society
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• v.14 no.2
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• pp.373-383
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• 1999

The ($\alpha$,$\beta$)-metric is a Finsler metric which is constructed from a Riemannian metric $\alpha$ and a differential 1-from $\beta$;it has been sometimes treated in theoretical physics. The condition for a Finsler space with an ($\alpha$,$\beta$)-metric L($\alpha$,$\beta$) to be projectively flat was given by Matsumoto [11]. The present paper is devoted to studying the condition for a Finsler space with L=$\alpha$\ulcorner$\beta$\ulcorner or L=$\alpha$+$\beta$\ulcorner/$\alpha$ to be projectively flat on the basis of Matsumoto`s results.

• Journal of the Korean Mathematical Society
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• v.39 no.2
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• pp.277-287
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• 2002

Let B be the open unit ball with center 0 in the complex space $C^n$. For each q>0, B$_{q}$ consists of holomorphic functions f : B longrightarrow C which satisfy sup z $\in$ B $(1-\parallel z \parallel^2)^q\parallel\nabla f(z)\parallel < \infty$ In this paper, we will show that functions in weighted Bloch spaces $B_{q}$ (0 < q < 1) satifies the following Lipschitz type result for Bergman metric $\beta$: ｜f(z)-f($\omega$)｜< $C\beta$(z, $\omega$) for some constant C.

• The Pure and Applied Mathematics
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• v.25 no.2
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• pp.73-94
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• 2018

We introduce some new type of admissible mappings and prove a coupled coincidence point theorem by using newly defined concepts for generalized compatible pair of mappings satisfying ${\alpha}-{\psi}$ contraction on partially ordered metric spaces. We also prove the uniqueness of a coupled fixed point for such mappings in this setup. Furthermore, we give an example and an application to integral equations to demonstrate the applicability of the obtained results. Our results generalize some recent results in the literature.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.417-428
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• 2016

We discuss and obtain some existence theorems of unique point of coincidence for two mappings satisfying ${\varphi}$-contractive conditions or ${\psi}$-${\phi}$-contractive conditions determined by semi-continuous functions on non-complete 2-metric spaces, in which the mappings do not satisfy commutativity and uniform boundedness. The obtained results generalize and improve many well-known and corresponding conclusions.

• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.83-89
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• 1993

Applications of the classical Knaster-Kuratowski-Mazurkiewicz theorem [KKM] and the fixed point theory of multifunctions defined on convex subsets of topological vector spaces have been greatly improved by adopting the concept of convex spaces due to Lassonde[L]. Recently, this concept has been extended to pseudo-convex spaces, contractible spaces, or spaces having certain families of contractible subsets by Horvath[H1-4]. In the present paper we give a far-reaching generalization of the best approximation theorem of Ky Fan[F1, 2] to pseudo-metric spaces and improved versions of the well-known fixed point theorems due to Brouwer [B] and Schauder [S] for spaces having certain families of contractible subsets. Our basic tool is a generalized Fan-Browder type fixed point theorem in our previous works [P3, 4].

• East Asian mathematical journal
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• v.16 no.2
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• pp.175-181
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• 2000

In this paper we show fixed point theorems related with the diameter of orbit on metric spaces. The results presented in this paper extend, improve and unify the results of $Heged\"{u}s$ [1], Kim, Kim, Leem and Ume [2], Kim and Leem [3], Ohta and Nikaido [4] and $Taskovi\'{c}$ [5].

• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.377-384
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• 2012

In this paper some properties of sequentially closed sets and $k$-closed sets in a topological space are discussed, it is shown that a space is a $k$-quotient image of a metric space if and only if its each sequentially closed set is $k$-closed, and some related examples about connectedness are obtained.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.485-492
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• 2005

In this paper, we obtain some common fixed point theorems for fuzzy mappings in complete metric linear spaces.

• East Asian mathematical journal
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• v.16 no.2
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• pp.183-197
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• 2000