Vol. 2 No. 1 (2018): Vol 2, Iss 1, Year 2018
Articles

A Fixed Point Theorem for Asymptotic φ−Contraction in Ultrametric Space

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  • Pavana Devassykutty,
  • Pitchaimani M
Pavana Devassykutty
Ramanujan Institute for Advanced Study in Mathematics University of Madras Chepauk, Chennai-600 005, S.India.
Pitchaimani M
Ramanujan Institute for Advanced Study in Mathematics University of Madras Chepauk, Chennai-600 005, S.India
DOI: https://doi.org/10.26524/cm25
Published June 30, 2018
Keywords
  • Fixed point, Asymptotic contraction, Ultra metric space.
How to Cite
Devassykutty, P., & M, P. (2018). A Fixed Point Theorem for Asymptotic φ−Contraction in Ultrametric Space. Journal of Computational Mathematica, 2(1), 41-47. https://doi.org/10.26524/cm25

Abstract

Recently, Kirk introduced an asymptotic form of Boyd-Wong fixed point theorem in metric space. In this paper, we have proved a fixed point theorem for asymptotic φ−Contraction in ultrametric space setting. We assume a weaker limit condition instead of boundedness of an orbit of the self map , which was an assumption in the hypothesis of Kirk’s theorem. Our result modifies the theorem given by Kirk in metric space.

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