• Bulletin of the Korean Mathematical Society
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• v.45 no.3
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• pp.467-475
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• 2008

The aim of the present paper is three fold. Firstly, we obtain common fixed point theorems for a pair of selfmaps satisfying nonexpansive or Lipschitz type condition by using the notion of pointwise R-weak commutativity but without assuming the completeness of the space or continuity of the mappings involved (Theorem 1, Theorem 2 and Theorem 3). Secondly, we generalize the results obtained in first three theorems for four mappings by replacing the condition of noncompatibility of maps with the property (E.A) and using the R-weak commutativity of type $(A_g)$ (Theorem 4). Thirdly, in Theorem 5, we show that if the aspect of noncompatibility is taken in place of the property (E.A), the maps become discontinuous at their common fixed point. We, thus, provide one more answer to the problem posed by Rhoades [11] regarding the existence of contractive definition which is strong enough to generate fixed point but does not forces the maps to become continuous.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.1027-1035
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• 2011

In this paper, we introduce the concept of generalized weak q-contractivity for multivalued maps defined on quasi-metric spaces. A new fixed point theorem for these maps is established. The convergene of iterate schem of the form $x_n+1\;{\in}\;Fx_n$ is investigated. And a new periodic point theorem for weakly q-contractive self maps of quasi-metric spaces is proved.

• The Pure and Applied Mathematics
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• v.10 no.3
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• pp.145-161
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• 2003

Weak commutativity of a pair of maps was introduced by Sessa [On a weak commutativity condition of mappings in fixed point considerations. Publ. Inst. Math. (Beograd) (N.S.) 32(40) (1982),149-153] in fixed point considerations. Thereafter a number of generalizations of this notion has been obtained. The purpose of this paper is to present a brief development of weaker forms of commuting maps, and to obtain two fixed point theorems for noncommuting and noncontinuous maps on noncomplete metric spaces.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.325-336
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• 2008

In this paper, we prove the weak and strong convergence of the three-step iterative scheme with errors to a common fixed point for two asymptotically nonexpansive mappings in a uniformly convex Banach space under a condition weaker than compactness. Our theorems improve and generalize some previous results.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.375-388
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• 2013

In this paper, we introduce an iterative sequence for finding solution of a system of mixed equilibrium problems and the set of fixed points of a nonexpansive mapping in Hilbert spaces. Then, the weak and strong convergence theorems are proved under some parameters controlling conditions. Moreover, we apply our result to fixed point problems, system of equilibrium problems, general system of variational inequalities, mixed equilibrium problem, equilibrium problem and variational inequality.

• Journal of the Chungcheong Mathematical Society
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• v.18 no.1
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• pp.51-64
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• 2005

The object of this paper is to prove two unique common fixed point theorems for a pair of a set-valued map and a self map satisfying a general contractive condition using orbital concept and weak-compatibility of the pair. One of these results generalizes substantially, the result of Dhage, Jennifer and Kang [4]. Simultaneously, its implications for two maps and one map improves and generalizes the results of Dhage [3], and Rhoades [11]. All the results of this paper are new.

• Korean Journal of Mathematics
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• v.21 no.1
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• pp.81-90
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• 2013

We investigate the bounded weak solutions for the Hamiltonian system with bounded nonlinearity decaying at the origin and periodic condition. We get a theorem which shows the existence of the bounded weak periodic solution for this system. We obtain this result by using variational method, critical point theory for indefinite functional.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.525-536
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• 2007

In this paper, we prove the weak and strong convergence of the Noor iterative scheme to a common fixed point for two asymptotically nonexpansive mappings in a uniformly convex Banach space under a condition weaker than compactness. Our theorems improve and generalize some previous results.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2011.06a
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• pp.817-818
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• 2011

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.51 no.11
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• pp.535-543
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• 2002

Modern power grids are becoming more and more stressed with the load demands increasing continually. Therefore large stressed power systems exhibit complicated dynamic behavior when subjected to small disturbance. Especially, it is needed to analyze special conditions which make small signal stability structure varied according to operating conditions. This paper shows that the relation between small signal stability structure varied according to operating conditions. This paper shows that the relation between small signal stability and operating conditions can be identified well using node-focus point and 1:1 resonance point. Also, the weak point which limits operating range is found by the analysis of resonance condition, and it is shown that reactive power compensation may solve the problem in the weak points. The proposed method is applied to test systems, and the results illustrate its capabilities.