Fixed points of non-Newtonian contraction mappings on non-Newtonian metric spaces
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 Classification26A06 54H25 47H10 11U10
KeywordsNon-Newtonian calculus non-Newtonian topological structures fixed point non-Newtonian contraction mapping
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- 2.A. F. Çakmak and F. Başar, Some new results on sequence spaces with respect to non-Newtonian calculus. J. Inequal. Appl. 2012 (2012), doi: 10.1186/1029-242X-2012-228, 17 pages.
- 3.Choudhary B., Nanda S.: Functional Analysis with Applications. John Wiley and Sons, New York (1990)Google Scholar
- 4.M. Grossman and R. Katz, Non-Newtonian Calculus. Lowell Technological Institute, 1972.Google Scholar
- 5.X. He, M. Song and D. Chen, Common fixed points for weak commutative mappings on a multiplicative metric space. Fixed Point Theory Appl. 2014 (2014), doi: 10.1186/1687-1812-2014-48, 9 pages.
- 6.M. Özavşar and A. C. Çevikel, Fixed points of multiplicative contraction mappings on multiplicative metric spaces. Preprint, arXiv:1205.5131v1 [matn.GN], 2012.
- 7.W. Takahashi, Nonlinear Functional Analysis: Fixed Point Theory and Its Applications. Yokohama Publishers, Yokohama, 2000.Google Scholar