Multi-valued \(F\)-contractions and the solution of certain functional and integral equations. (English) Zbl 1340.54080

Sgroi, Margherita; Vetro, Calogero

Filomat 27, No. 7, 1259-1268 (2013).

Authors’ abstract: D. Wardowski in [Fixed Point Theory Appl., Article ID. 94, 6 p., (2012; Zbl 1310.54074)] introduced a new concept of contraction and proved a fixed point theorem which generalizes the Banach contraction principle. Following this direction of research, we 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.

Reviewer: Marko Nedeljkov (Novi Sad)

MSC:

54H25

Fixed-point and coincidence theorems (topological aspects)