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Fixed points of non-Newtonian contraction mappings on non-Newtonian metric spaces

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Abstract

The study of non-Newtonian calculi was started in 1972 by Grossman and Katz. These calculi provide an alternative to the classical calculus and they include the geometric, anageometric and bigeometric calculi, etc. Recently, Çakmak and Başar (2002) have studied the concept of non-Newtonian metric. Also they have given the triangle and Minkowski’s inequalities in the sense of non-Newtonian calculus. In this paper, we introduce a fixed point theory by defining some topological structures of the relevant non-Newtonian metric space.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Arts and Sciences, Gaziosmanpaşa University, Tokat, 60240, Turkey

    Demet Binbaşıoǧlu & Serkan Demiriz

  2. Department of Mathematics, Faculty of Sciences, Gazi University, 06500, Teknikokullar, Ankara, Turkey

    Duran Türkoǧlu

Authors
  1. Demet Binbaşıoǧlu
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  2. Serkan Demiriz
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  3. Duran Türkoǧlu
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Correspondence to Demet Binbaşıoǧlu.

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Binbaşıoǧlu, D., Demiriz, S. & Türkoǧlu, D. Fixed points of non-Newtonian contraction mappings on non-Newtonian metric spaces. J. Fixed Point Theory Appl. 18, 213–224 (2016). https://doi.org/10.1007/s11784-015-0271-y

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  • DOI: https://doi.org/10.1007/s11784-015-0271-y

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