• Journal of the Korean Mathematical Society
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• v.59 no.3
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• pp.549-570
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• 2022

In this paper, we study the Birkhoff's ergodic theorem on geodesic metric spaces, especially on Hadamard spaces, using the notion of weighted inductive means. Also, we study a deterministic weighted sequence for the weighted Birkhoff's ergodic theorem in Hadamard spaces.

• Korean Journal of Mathematics
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• v.18 no.1
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• pp.11-19
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• 2010

In this paper, several common fixed degree theorems of a sequence of fuzzy mappings defined on symmetric spaces are established.

• Bulletin of the Korean Mathematical Society
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• v.34 no.3
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• pp.359-370
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• 1997

In this paper we get the Morava K-theory of the double loop spaces of quarternionic Stiefel manifolds for an odd prime p by computing the Atiyah - Hirzebruch spectral sequence. We also get the homology with Z/(p) coefficients and analyze p torsion in the homology with Z coefficients.

• Korean Journal of Mathematics
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• v.27 no.4
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• pp.949-968
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• 2019

In this work, we characterize some matrix classes concerning the Binomial sequence spaces b^r,s_∞ and b^r,s_p, where 1 ≤ p < ∞. Moreover, by using the notion of Hausdorff measure of noncompactness, we characterize the class of compact matrix operators from b^r,s₀, b^r,s_c and b^r,s_∞ into c₀, c and ℓ_∞, respectively.

• Journal of the Korean Mathematical Society
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• v.48 no.6
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• pp.1125-1142
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• 2011

In this paper, we define some new sequence spaces of infinite matrices regarded as operators on $l_2$ by using algebraic properties of such the matrices under the Schur product multiplication. Some of their basic properties as well as duality and preduality are discussed.

• Journal of the Korean Mathematical Society
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• v.39 no.1
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• pp.149-161
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• 2002

We study the torsions in the integral homology of the double loop space of the compact simple Lie groups by determining the higher Bockstein actions on the homology of those spaces through the Bockstein lemma and computing the Bockstein spectral sequence.

• Communications of the Korean Mathematical Society
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• v.31 no.2
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• pp.277-294
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• 2016

The aim of this paper is to present the classical sets of sequences and related matrix transformations with respect to the b-metric. Also, we introduce the relationships between these sets and their classical forms with corresponding properties including convergence and completeness. Further we determine the duals of the new spaces and characterize matrix transformations on them into the sets of b-bounded, b-convergent and b-null sequences.

• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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• pp.847-860
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• 2006

In this paper, some new convergence theorems of the modified Ishikawa and Mann iterative sequences with errors for asymptotically set-valued pseudocontractive mappings in uniformly smooth Banach spaces are given.

• East Asian mathematical journal
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• v.19 no.1
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• pp.103-111
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• 2003

In this paper, we will discuss some sufficient and necessary conditions for modified Ishikawa iterative sequence with mixed errors to converge to fixed points for asymptotically quasi-nonexpansive mappings in Banach spaces. The results presented in this paper extend, generalize and improve the corresponding results in Liu [4,5] and Ghosh-Debnath [2].

• Kyungpook Mathematical Journal
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• v.53 no.2
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• pp.247-256
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• 2013

In this paper we have examined the spectra of the operator D($r$, 0, 0, $s$) on sequence spaces $c_0$ and $c$.