• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.399-410
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• 2016

In this paper, we study the relations between the Thurston metric and the hyperbolic metric on a closed surface of genus $g{\geq}2$. We show a rigidity result which says if there is an inequality between the marked length spectra of these two metrics, then they are isotopic. We obtain some inequalities on length comparisons between these metrics. Besides, we show certain distance distortions under conformal graftings, with respect to the $Teichm{\ddot{u}}ller$ metric, the length spectrum metric and Thurston's asymmetric metrics.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.685-702
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• 2023

This paper is concerned with fixed point results of a finite family of multi-valued Osilike-Berinde nonexpansive type mappings in hyperbolic spaces along with some numerical examples. Also strong convergence and ∆-convergence of a sequence generated by Alagoz iteration scheme are investigated.

• Kyungpook Mathematical Journal
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• v.48 no.3
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• pp.433-442
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• 2008

In this paper we consider a real hypersurface M in complex hyperbolic space $H_n\mathbb{C}$ satisfying $S{\phi}A\;=\;{\phi}AS$, where $\phi$, A and S denote the structure tensor, the shape operator and the Ricci tensor of M respectively. Moreover, we give a characterization of real hypersurfaces of type A in $H_n\mathbb{C}$ by such a commuting Ricci tensor.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.575-583
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• 2016

In this paper, we study the modified S-iteration process for asymptotic pointwise nonexpansive mappings in a uniformly convex hyperbolic metric space. We then prove the convergence of the sequence generated by the modified S-iteration process.

• Korean Journal of Mathematics
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• v.24 no.4
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• pp.647-662
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• 2016

In this paper, we study Lipschitz continuous, the boundedness and compactness of the composition operator $C_{\phi}$ acting between the general hyperbolic Bloch type-classes ${\mathcal{B}}^{\ast}_{p,{\log},{\alpha}}$ and general hyperbolic Besov-type classes $F^{\ast}_{p,{\log}}(p,q,s)$. Moreover, these classes are shown to be complete metric spaces with respect to the corresponding metrics.

• Magazine of korean Tunnelling and Underground Space Association
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• v.21 no.1
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• pp.27-31
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• 2019

• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.71-85
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• 1997

In this paper we find sufficient conditions of existence of the nonlinear ODE ($P_{\epsilon}$) which is induced by the nonlinear hyperbolic system of conservation laws in several space variables.

• Bulletin of the Korean Mathematical Society
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• v.46 no.4
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• pp.713-720
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• 2009

We find all left-invariant minimal unit vector fields and strongly normal unit vector fields on a Lie group which is isometric to the hyperbolic space.

• Communications of the Korean Mathematical Society
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• v.30 no.3
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• pp.209-219
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• 2015

In this article, we first give metric version of an iteration scheme of Agarwal et al. [1] and approximate fixed points of two finite families of nonexpansive mappings in hyperbolic spaces through this iteration scheme which is independent of but faster than Mann and Ishikawa scheme. Also we consider case of three finite families of nonexpansive mappings. But, we need an extra condition to get convergence. Our convergence theorems generalize and refine many know results in the current literature.

• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.63-82
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• 2011

On the hyperbolic space $D^n$, codimension-one totally geodesic foliations of class $C^k$ are classified. Except for the unique parabolic homogeneous foliation, the set of all such foliations is in one-one correspondence (up to isometry) with the set of all functions z : [0, $\pi$] $\rightarrow$ $S^{n-1}$ of class $C^{k-1}$ with z(0) = $e_1$ = z($\pi$) satisfying |z'(r)| ${\leq}1$ for all r, modulo an isometric action by O(n-1) ${\times}\mathbb{R}{\times}\mathbb{Z}_2$. Since 1-dimensional metric foliations on $D^n$ are always either homogeneous or flat (that is, their orthogonal distributions are integrable), this classifies all 1-dimensional metric foliations as well. Equations of leaves for a non-trivial family of metric foliations on $D^2$ (called "fifth-line") are found.