Abstract
Starting from two extensions of the Banach contraction principle due to Ćirić (1974) and Wardowski (2012), in the present paper we introduce the concepts of Ćirić type ψ F -contraction and ψ F -quasicontraction on a metric space and give some sufficient conditions under which the respective mappings are Picard operators. Some known fixed point results from the literature can be obtained as particular cases.
Highlights
Introduction and PreliminariesThe Banach contraction principle, known as Banach-Caccioppoli-Picard, is an important tool in the theory of metric spaces, having a crucial role in the study of many diverse disciplines.Starting from The Banach contraction principle, metrical fixed point theory has developed intensively in recent decades, both by generalizing the contractions and the metric spaces, and by extending the applications
Our paper is part of this effort by providing some fixed point results for a new kind of contraction map
The fixed point result obtained by Ćirić [1] is a consequence of the previous theorem
Summary
Introduction and PreliminariesThe Banach contraction principle, known as Banach-Caccioppoli-Picard, is an important tool in the theory of metric spaces, having a crucial role in the study of many diverse disciplines.Starting from The Banach contraction principle, metrical fixed point theory has developed intensively in recent decades, both by generalizing the contractions and the metric spaces, and by extending the applications. Proved that, if the space X is T-orbitally complete, T is a P.O. This fixed point result generalizes that one obtained by Hardy and Rogers [2]. [3] Bessenyei called weak φ-quasicontraction (respectively strong φ-quasicontraction) a self-mapping T on a metric space X of bounded orbits and, for every x, y ∈ X, d( Tx, Ty) ≤ φ diam O( x, y) d( Tx, Ty) ≤ φ diam { x, y, Tx, Ty} ), (3)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
