• East Asian mathematical journal
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• v.28 no.5
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• pp.569-578
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• 2012

In this paper, the necessary and sufficient conditions for the strong convergence of a modified Mann iteration process to a fixed point of an asymptotically demicontractive mapping in real Banach spaces are considered. Presented results improve and extend the results of Igbokwe [3], Liu [4], Moore and Nnoli [6] and Osilike [7].

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.161-173
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• 2009

In this paper, we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of the variational inequality for an inverse-strongly monotone mapping and the set of solutions of an equilibrium problem in a Hilbert space. We show that the iterative sequence converges strongly to a common element of the three sets. The results of this paper extend and improve the corresponding results announced by many others.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.207-211
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• 2014

The aim of this paper is to prove the next result. Let n > 1 be an integer and let R be a n!-torsion free semiprime ring. Suppose that f : R ${\rightarrow}$ R is an additive mapping satisfying the relation [f(x), $x^n$] = 0 for all $x{\in}R$. Then f is commuting on R.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1297-1302
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• 2013

We prove that the mapping class group of a non-Haken orientable irreducible 3-manifold is finite and we show that the quotient group of the mapping class group by the rotation group is virtually torsion-free if the manifold does not have 2-sphere boundary components.

• Honam Mathematical Journal
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• v.31 no.2
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• pp.219-231
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• 2009

For a mapping satisfying the inequality ${\parallel}{\lambda}f(x)+2{\lambda}f(y)+2f({\lambda}z){\parallel}{\leq}{\parallel}2f({\lambda}({\frac{2}{x}}+y+z)){\parallel}+{\phi}(x,y,z)$, we will study the stability problem of this mapping.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.507-518
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• 2016

The aim of this paper is to prove some strong convergence theorems for the modified Ishikawa iteration process involving a pair of a generalized asymptotically nonexpansive single-valued mapping and a quasi-nonexpansive multi-valued mapping in the framework of $\mathbb{R}$-trees under the gate condition.

• Journal of the Korean Mathematical Society
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• v.49 no.1
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• pp.187-200
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• 2012

In this paper, we introduced a new extended extragradient iteration algorithm for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of equilibrium problems for a monotone and Lipschitz-type continuous mapping. And we show that the iterative sequences generated by this algorithm converge strongly to the common element in a real Hilbert space.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1419-1431
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• 2018

Let $f=h+{\bar{g}}$ be a harmonic mapping of the unit disk ${\mathbb{D}}$ with the holomorphic part h satisfying that h is injective and $h({\mathbb{D}})$ is an M-linearly connected domain. In this paper, we obtain the sufficient and necessary conditions for f to be bi-Lipschitz, which is in particular, quasiconformal. Moreover, some distortion theorems are also obtained.

• Honam Mathematical Journal
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• v.31 no.4
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• pp.497-504
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• 2009

We introduce the concepts of M-preclosed graph and M$^*$-preopen mapping on spaces with minimal structures and investigate some properties of M$^*$-preopen mapping. We also investigate the relationships between M-precontinuous mappings and several types of m-compactness.

• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.279-296
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• 2012

In this paper, we define a generalized duality mapping, which is a generalization of the normalized duality mapping and using this, we extend the notion of a generalized projection and study their properties. Also we construct an approximating fixed point sequence using the generalized projection with the generalized duality mapping and prove its strong convergence.