Generalized contractions in partially ordered metric spaces

Agarwal, Ravi P.; El-Gebeily, M. A.; O’Regan, Donal

doi:10.1080/00036810701556151

Cited by 411 publications

(254 citation statements)

References 3 publications

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“…Then many fixed point theorists such as Abbas et al [1], Agarwal et al [3],Ćirić et al [5], Kumam et al [6], Nashine and Altun [8] and O'Regan and Petruşel [11] focused on this interesting result and obtained a lot of generalizations and variants. For example, taking the regularity of the space, which will be define thereinafter, instead of continuity of T, Nieto [9] obtained a parallel result.…”

Section: Introductionmentioning

confidence: 99%

Fixed Points of Ordered F-Contractions

Durmaz¹,

Mınak²

2016

HJMS

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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.

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