• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권3호
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• pp.249-267
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• 2023

This manuscript is divided into three segments. In the first segment, we prove a unique common fixed point theorem satisfying generalized weak contraction on partially ordered metric spaces and also give an example to support our results presented here. 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 integral equation as an application. Our results generalize, extend and improve several well-known results of the existing literature.

• Journal of applied mathematics & informatics
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• 제36권1_2호
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• pp.69-79
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• 2018

The Euclid metric is well-known and there are many results on the space with that metric. But there are many other metrics which gives more practical and useful results in the plane. In this paper, we introduce new metric function in the plane, which is more useful in city with subway. Finally we generalize to the general metric space and introduce a new metric on ${\mathbb{R}}^n$.

• 대한수학회보
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• 제53권1호
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• pp.61-81
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• 2016

In this paper, we prove some existence and uniqueness results on coincidence points for g-monotone mappings satisfying linear as well as generalized nonlinear contractivity conditions in ordered metric spaces. Our results generalize and extend two classical and well known results due to Ran and Reurings (Proc. Amer. Math. Soc. 132 (2004), no. 5, 1435-1443) and Nieto and $Rodr{\acute{i}}guez$-$L{\acute{o}}pez$ (Acta Math. Sin. 23 (2007), no. 12, 2205-2212) besides similar other ones. Finally, as an application of one of our newly proved results, we establish the existence and uniqueness of solution of a first order periodic boundary value problem.

• East Asian mathematical journal
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• 제29권3호
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• pp.303-314
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• 2013

In this paper, we introduce an iterative scheme for finding a common element of the set of solutions of a generalized equilibrium problem and the set of common fixed points of a finite family of asymptotically ${\kappa}$-strict pseudo-contractions in Hilbert spaces. Weak and strong convergence theorems are established for the iterative scheme.

• 한국수학사학회지
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• 제17권3호
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• pp.1-12
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• 2004

해석학에서는 위상 구조와 고른 구조를 거리 공간에서 다루었기 때문에 많은 혼동이 있었다. 거리 공간의 개념은 위상 구조로 일반화되었지만 '고르다'는 개념은 그 후에 앙드레 베이유에 의해서 고른 구조로 일반화되었다. 우리는 먼저 베이유의 삶과 그의 수학적 업적을 살피고 고른 구조의 역사와 발달에 대해서 알아볼 것이다.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제25권2호
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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.

• 충청수학회지
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• 제21권4호
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• pp.527-532
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• 2008

We compare a coding space which has an ultra metric with the unit interval which has an associated generalized dyadic expansion. The two spaces are not homeomorphic but dimensionally equivalent in the sense that the Hausdorff and packing dimensions of the corresponding distribution sets in the two spaces coincide.

• East Asian mathematical journal
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• 제25권1호
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• pp.1-10
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• 2009

In this paper, we prove some common fixed point theorems of compatible mappings under the generalized contractive type in metric spaces and also give some examples to illustrate our main theorems. This results extend the results of several authors.

• Nonlinear Functional Analysis and Applications
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• 제27권2호
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• pp.261-269
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• 2022

The purpose of this paper is to introduce a new generalization class of cyclic mappings, called cyclic generalized 𝜑-weak contraction and obtain a corresponding best proximity point theorem for this cyclic mapping under certain conditions.

• East Asian mathematical journal
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• 제16권2호
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• pp.339-354
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• 2000