Fixed points of ordered F-contractions

Year 2016, Volume: 45 Issue: 1, 15 - 21, 01.02.2016

Gonca Durmaz , Gülhan Mınak İshak Altun

Abstract

In his recent paper, Wardowski [16] introduced the concept of Fcontraction, which is a proper generalization of ordinary contraction on
a complete metric space. Then, some generalizations of F-contractions
including multivalued case are obtained in [2, 4, 7, 13]. In this paper,
by considering both F-contractions and fixed point result on ordered
metric spaces, we introduce a new concept of ordered F-contraction on
ordered metric space. Then, we give a fixed point theorem for such
mapping. To support our result, we give an example showing that our
main theorem is applicable, but both results of Ran and Reurings [12]
and Wardowski [16] are not. 

Keywords

Fixed point, F-contraction, ordered F-contraction, Complete metric space

References

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