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Cone metric spaces and fixed point theorems in diametrically contractive mappings

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Abstract

In this paper, some topological concepts and definitions are generalized to cone metric spaces. It is proved that every cone metric space is first countable topological space and that sequentially compact subsets are compact. Also, we define diametrically contractive mappings and asymptotically diametrically contractive mappings on cone metric spaces to obtain some fixed point theorems by assuming that our cone is strongly minihedral.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Arts, Gazi University, Teknikokullar, Ankara, 06500, Turkey

    Duran Turkoglu

  2. Department of Mathematics, Institute of Science and Technology, Gazi University, Ankara, 06500, Turkey

    Muhib Abuloha

Authors
  1. Duran Turkoglu
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  2. Muhib Abuloha
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Correspondence to Duran Turkoglu.

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Supported by the Scientific and Technological Research Council of Turkey (TUBITAK-Turkey)

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Turkoglu, D., Abuloha, M. Cone metric spaces and fixed point theorems in diametrically contractive mappings. Acta. Math. Sin.-English Ser. 26, 489–496 (2010). https://doi.org/10.1007/s10114-010-8019-5

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  • DOI: https://doi.org/10.1007/s10114-010-8019-5

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