Integral type contractions in partial metric spaces


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ÖZTÜRK V., TÜRKOĞLU A. D.

International Conference of Mathematical Sciences 2018, ICMS 2018, İstanbul, Turkey, 31 July - 06 August 2018, vol.2086 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 2086
  • Doi Number: 10.1063/1.5095116
  • City: İstanbul
  • Country: Turkey
  • Keywords: fixed point, F-contaction, integral type contraction, partial metric

Abstract

© 2019 Author(s).It is known that history of mathematics is old as history of humanity. Mathematics covered a distance significantly from ancient age to now. Recently, there are many important works for modern mathematics([6],[8]). Let X be a nonempty set and f: X → X be a mapping. If f (x) = x, for some x ? X, then x is fixed point of f. Banach fixed point theorem was introduced in 1922 in complete metric spaces as "(X, d) be a complete metric space and f: X → X be a self-mapping. If there exists 0 ≤ k < 1 such that d (fx, fy) ≤ kd (x, y) for all x, y ? X. Then f has unique fixed point"([1]). Partial metric spaces were introduced by Matthews (1994) as a generalisation of usual metric spaces where the self distance for any point need not be equal to zero. In this work, we define generalized integral type F-contractions and prove common fixed point theorems for four mappings satisfying these types contractions in partial metric spaces.