• 한국수학교육학회지시리즈B:순수및응용수학
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• 제28권1호
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• pp.61-69
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• 2021

In this paper, we introduce a new three-step iterative scheme for three finite families of nonexpansive mappings in hyperbolic spaces. And, we establish a strong convergence and a ∆-convergence of a given iterative scheme to a common fixed point for three finite families of nonexpansive mappings in hyperbolic spaces. Our results generalize and unify the several main results of [1, 4, 5, 9].

• Korean Journal of Mathematics
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• 제27권4호
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• pp.929-947
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• 2019

In the present paper, we investigate the convergence, equivalence of convergence, rate of convergence and data dependence results using a three step iteration process for mappings satisfying certain contractive condition in hyperbolic spaces. Also we give nontrivial examples for the rate of convergence and data dependence results to show effciency of three step iteration process. The results obtained in this paper may be interpreted as a refinement and improvement of the previously known results.

• 대한수학회논문집
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• 제14권1호
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• pp.171-177
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• 1999

We study some properties of Toeplitz operators on the Bergman spaces B\ulcorner(H\ulcorner), where H\ulcorner={x+iy : y>r}. We consider the pseudo-hyperbolic disk and the covering property. We also obtain some characterizations of compact Toeplitz operators.

• Kyungpook Mathematical Journal
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• 제46권1호
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• pp.1-9
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• 2006

M. Reni has shown that there are at most nine mutually inequivalent knots in the 3-sphere whose 2-fold branched covering spaces are mutually homeomorphic, hyperbolic 3-manifolds. By observing that the Z-homology sphere version of M. Reni's result still holds, M. Mecchia and B. Zimmermann showed that there are exactly nine mutually inequivalent, knots in Z-homology 3-spheres whose 2-fold branched covering spaces are mutually homeomorphic, hyperbolic 3-manifolds, and conjectured that there exist exactly nine mutually inequivalent, knots in the true 3-sphere whose 2-fold branched covering spaces are mutually homeomorphic, hyperbolic 3-manifolds. Their proof used an argument of AID imitations published in 1992. The main result of this paper is to solve their conjecture affirmatively by combining their argument with a theory of strongly AID imitations published in 1997.

• Nonlinear Functional Analysis and Applications
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• 제28권3호
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• pp.623-646
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• 2023

In this article, we introduce the hyperbolic space version of a faster iterative algorithm. The proposed iterative algorithm is used to approximate the common fixed point of three multi-valued almost contraction mappings and three multi-valued mappings satisfying condition (E) in hyperbolic spaces. The concepts weak w²-stability involving three multi-valued almost contraction mappings are considered. Several strong and △-convergence theorems of the suggested algorithm are proved in hyperbolic spaces. We provide an example to compare the performance of the proposed method with some well-known methods in the literature.

• Kyungpook Mathematical Journal
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• 제60권2호
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• pp.375-385
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• 2020

Minkowski spaces have long been investigated with respect to certain properties and substructues such as hyperbolic curves, hyperbolic angles and hyperbolic arc length. In 2009, based on these properties, Chung et al. [3] defined the basic concepts of special relativity, and thus; they interpreted the geometry of the Minkowski spaces. Then, in 2017, E. Nesovic [6] showed the geometric meaning of pseudo angles by interpreting the angle among the unit timelike, spacelike and null vectors on the Minkowski plane. In this study, we show that hyperbolic angle depends on time, t. Moreover, using this fact, we investigate the angles between the unit timelike and spacelike vectors.

• Nonlinear Functional Analysis and Applications
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• 제28권3호
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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.

• 대한수학회지
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• 제36권3호
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• pp.621-631
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• 1999

In this paper we briefly describe the geometry of the Cayley hyperbolic plane and we show that every uniform lattice in quaternionic space cannot be deformed in the Cayley hyperbolic 2-plane. We also describe the nongeometric bending deformation by developing the theory of the Cartan angular invariant for quaternionic hyperbolic space.

• 대한수학회보
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• 제51권1호
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• pp.13-27
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• 2014

The purpose of this paper is to derive a perturbation theory of evolution systems of the hyperbolic second order hyperbolic equations. We give an example of a partial functional equation as an application of the preceding result in case of the mixed problems for hyperbolic equations of second order with unbounded principal operators.

• 대한수학회논문집
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• 제13권1호
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• pp.171-179
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• 1998

In this paper, we establish Trotted-Kato type convergence theoren for nonlinear semigroups generated by coaccretive operators in a hyperbolic space.