• 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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제23권2호
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• pp.201-201
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• 2016

• 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.

• 대한수학회지
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• 제57권6호
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• pp.1435-1449
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• 2020

In this article we make a local classification of n-dimensional Riemannian manifolds (M, g) with harmonic curvature and less than four Ricci eigenvalues which admit a smooth non constant solution f to the following equation $$(1)\hspace{20}{\nabla}df=f(r-{\frac{R}{n-1}}g)+x{\cdot} r+y(R)g,$$ where ∇ is the Levi-Civita connection of g, r is the Ricci tensor of g, x is a constant and y(R) a function of the scalar curvature R. Indeed, we showed that, in a neighborhood V of each point in some open dense subset of M, either (i) or (ii) below holds; (i) (V, g, f + x) is a static space and isometric to a domain in the Riemannian product of an Einstein manifold N and a static space (W, gW, f + x), where gW is a warped product metric of an interval and an Einstein manifold. (ii) (V, g) is isometric to a domain in the warped product of an interval and an Einstein manifold. For the proof we use eigenvalue analysis based on the Codazzi tensor properties of the Ricci tensor.

• East Asian mathematical journal
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• 제32권3호
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• pp.333-354
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• 2016

We present coincidence point theorem for g-non-decreasing mappings satisfying generalized nonlinear contraction on partially ordered metric spaces. We show how multidimensional results can be seen as simple consequences of our unidimensional coincidence point theorem. We also obtain the coupled coincidence point theorem for generalized compatible pair of mappings $F,G:X^2{\rightarrow}X$ by using obtained coincidence point results. Furthermore, an example and an application to integral equation are also given to show the usability of obtained results. Our results generalize, modify, improve and sharpen several well-known results.

• Journal of applied mathematics & informatics
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• 제38권5_6호
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• pp.507-518
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• 2020

In this article, we establish some fixed point results in G-metric spaces using the modified JS-G-contractions and we provide some suitable examples to support the results. Also, we give an application to solve an integral equation.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제25권4호
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• pp.279-295
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• 2018

We study the existence and uniqueness of fixed point for isotone mappings of any number of arguments under Geraghty-type contraction on a complete metric space endowed with a partial order. As an application of our result we study the existence and uniqueness of the solution to a nonlinear Fredholm integral equation. Our results generalize, extend and unify several classical and very recent related results in the literature in metric spaces.

• 대한수학회논문집
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• 제12권4호
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• pp.999-1006
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• 1997

We proved that if a fibred Riemannian space $\tilde{M}$ with cosymplectic structure is conformally flat, then $\tilde{M}$ is the locally product manifold of locally Euclidean spaces, that is locally Euclidean. Moreover, we investigated the fibred Riemannian space with cosymplectic structure when the Riemannian metric $\tilde{g}$ on $\tilde{M}$ is Einstein.

• 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.

• 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.