Cone Metric Spaces and Fixed Point Theorems in Diametrically Contractive Mappings
Acta Mathematica Sinica, English Series
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Acta Mathematica Sinica, English Series  2010, Vol. 26 Issue (3): 489-496    DOI: 10.1007/s10114-010-8019-5
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Cone Metric Spaces and Fixed Point Theorems in Diametrically Contractive Mappings
Duran TURKOGLU1, Muhib ABULOHA2
1. Department of Mathematics, Faculty of Science and Arts, Gazi University, Teknikokullar,Ankara 06500, Turkey;
2. Department of Mathematics, Institute of Science and Technology, Gazi University,Ankara 06500, Turkey
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Abstract In this paper, some topological concepts and definitions are generalized to cone metricspaces. It is proved that every cone metric space is first countable topological space and that sequentiallycompact subsets are compact. Also, we define diametrically contractive mappings and asymptoticallydiametrically contractive mappings on cone metric spaces to obtain some fixed point theorems byassuming that our cone is strongly minihedral.
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Received: 2008-01-15;
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Supported by the Scientific and Technological Research Council of Turkey (TUBITAK-Turkey)

Cite this article:   
. Cone Metric Spaces and Fixed Point Theorems in Diametrically Contractive Mappings[J]. Acta Mathematica Sinica, English Series, 2010, 26(3): 489-496.
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http://www.actamath.com/Jwk_sxxb_en//EN/10.1007/s10114-010-8019-5      or     http://www.actamath.com/Jwk_sxxb_en//EN/Y2010/V26/I3/489
 
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[3] Abbas, M., Jungck, G.: Common fixed point results for noncommuting mappings without continuity in cone metric spaces. J. Math. Anal. Appl., 341(1), 416-420 (2008)
[4] Xu, H. K.: Diametrically contractive mappings. Bulletin of the Australian Mathematical Society, 70(3), 463-468 (2004)
[5] Deimling, K.: Nonlinear Functional Analysis, Springer-Verlag, Berlin, 1985
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