Multi-valued F-contractions and the solutions of certain functional and integral equations

By M. Sgroi, Calogero Vetro. 2013

185 citations recorded by the source corpus.

Wardowski (Fixed Point Theory Appl., 2012:94) introduced a new concept of contraction and proved a fixed point theorem which generalizes Banach contraction principle. Following this direction of research, we will present some fixed point results for closed multi-valued F-contractions or multi-valued mappings which satisfy an F-contractive condition of Hardy-Rogers-type, in the setting of complete metric spaces or complete ordered metric spaces. An example and two applications, for the solution of certain functional and integral equations, are given to illustrate the usability of the obtained results.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/084c3230ea528ccd8bb048a15f7923a2a71814c3

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In Geometry and Topology

Citations in the corpus

A survey: F-contractions with related fixed point results (2020, background): “Sgroi, Vetro (2013) [82] First of all, we recall some properties of multivalued mappings.”
Common fixed point results for new Ciric-type rational multivalued F-contraction with an application (2018, background): “[30] established fixed point theorems for multivalued F -contraction condition and obtained the solution of certain functional and integral equations, which was a proper generalization of some multivalued fixed point theorems including Nadler’s theorem [23].”
On common fixed points for α−F -contractions and applications (2016, unknown): “2 have been generalized in many directions, for more details see [1, 11, 16, 18, 19, 22].”