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Coincidence and common fixed points of hybrid contractions

Part of: Connections with other structures, applications

Published online by Cambridge University Press:  09 April 2009

M. S. Khan ,
Y. J. Cho ,
W. T. Park  and
T. Mumtaz
M. S. Khan
Affiliation:
Sultan Qaboos University, Department of Mathematics and Computing, College of Science, P.O. Box 32486, Al-Khod, Muscat, Sultanate of, Oman
Y. J. Cho
Affiliation:
Gyeongsang National University, Jinju 660-701, Korea
W. T. Park
Affiliation:
Gyeongsang National University, Jinju 660-701, Korea
T. Mumtaz
Affiliation:
Aligarh Muslim University, Aligarh 202002, India
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Abstract

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In this paper, we show the existence of solutions of functional equations fix ∈ Sx ∪ Tx and x = fix ∈ Sx ∪ Tx under certain nonlinear hybrid contraction and asymptotic regularity conditions, generalize and improve a recent result due to Kaneko concerning common fixed points of multivalued mappings weakly commuting with a single-valued mapping and satisfying a generalized contraction type. Some related results are also obtained.

Keywords

Coincidence and common fixed pointsHausdorff metricorbital completeproximinal subsets and weakly commuting mappings.

MSC classification

Secondary: 54H25: Fixed-point and coincidence theorems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 55 , Issue 3 , December 1993 , pp. 369 - 385
Copyright
Copyright © Australian Mathematical Society 1993

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