• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.579-590
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• 2005

In this paper we derive certain sufficient conditions for starlikeness and strongly starlikeness of analytic functions in the unit disk. Our results generalize and refine the related results due to Li and Owa[l, 2] and Ramesha et al.[5]. Some other new results are also given.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.605-615
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• 2000

Let E be a real Banach space with property (U,${\lambda}$,m+1,m);${\lambda}{\ge}$0; m${\in}N$, and let C be a nonempty closed convex and bounded subset of E. Suppose T: $C{\leftrightarro}C$ is a strongly accretive map, It is proved that each of the two well known fixed point iteration methods( the Mann and Ishikawa iteration methods.), under suitable conditions , converges strongly to a solution of the equation Tx=f.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.329-341
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• 2005

In this paper, we introduce new random iterative sequences with errors approximating a unique random common fixed point for three random set-valued strongly pseudo-contractive mappings and show the convergence of the random iterative sequences with errors by using an approximation method in real uniformly smooth separable Banach spaces. As applications, we study the existence of random solutions for some kind of random nonlinear operator equations group in separable Hilbert spaces.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.125-134
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• 2013

An element in a ring R is strongly clean provided that it is the sum of an idempotent and a unit that commutate. In this note, several necessary and sufficient conditions under which a $2{\times}2$ matrix over an integral domain is strongly clean are given. These show that strong cleanness over integral domains can be characterized by quadratic and Diophantine equations.

• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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• pp.399-410
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• 2003

The purpose of the present paper is to introduce some new subclasses of strongly close-to-convex functions in the open unit disk defined by multiplier transformations and study their properties. Our results include several previous known results as special cases.

• Journal of the Korean Institute of Intelligent Systems
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• v.12 no.6
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• pp.565-570
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• 2002

We introduce the concepts of fuzzy H-continuity and fuzzy strongly closed graph, respectively and investigate some of their properties.

• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.477-485
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• 1997

Let E be a smooth Banach space. Suppose T:$E \rightarrow E$ is a strongly accretive map. It is proved that each of the two well known fixed point iteration methods (the Mann and ishikawa iteration methods), under suitable conditions converges strongly to a solution of the equation $T_x=f$.

• 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.48 no.3
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• pp.637-646
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• 2011

Cho and Kim [4] and Kim [6] introduced the concept of the competition index of a digraph. Cho and Kim [4] and Akelbek and Kirkland [1] also studied the upper bound of competition indices of primitive digraphs. In this paper, we study the upper bound of competition indices of strongly connected digraphs. We also study the relation between competition index and ordinary index for a symmetric strongly connected digraph.

• Korean Journal of Mathematics
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• v.17 no.4
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• pp.461-471
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• 2009

Let ${\Omega}$ be a bounded subset of $R^n$ with smooth boundary and H be a Sobolev space $W_0^{1,2}({\Omega})$. Let $I{\in}C^{1,1}$ be a strongly definite functional defined on a Hilbert space H. We investigate the conditions on which the functional I satisfies the Palais-Smale condition. Palais-Smale condition is important for determining the critical points for I by applying the critical point theory.