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

  • Demet Binbaşıoǧlu
  • Serkan Demiriz
  • Duran Türkoǧlu
Article

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.

Mathematics Subject Classification

26A06 54H25 47H10 11U10 

Keywords

Non-Newtonian calculus non-Newtonian topological structures fixed point non-Newtonian contraction mapping 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  • Demet Binbaşıoǧlu
    • 1
  • Serkan Demiriz
    • 1
  • Duran Türkoǧlu
    • 2
  1. 1.Department of Mathematics, Faculty of Arts and SciencesGaziosmanpaşa UniversityTokatTurkey
  2. 2.Department of Mathematics, Faculty of SciencesGazi UniversityTeknikokullarTurkey

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