\(F_{m}\)-contractive and \(F_{m}\)-expanding mappings in \(M\)-metric spaces

Volume 18, Issue 3, pp 262--271 http://dx.doi.org/10.22436/jmcs.018.03.02 Publication Date: March 22, 2018       Article History


Nabil Mlaiki - Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia


Inspired by the work of Górnicki in his recent article [J. Górnicki, Fixed Point Theory Appl., \({\bf 2017}\) (2017), 10 pages], where he introduced a new class of self mappings called \(F\)-expanding mappings, in this paper we introduce the concept of \(F_{m}\)-contractive and \(F_{m}\)-expanding mappings in \(M\)-metric spaces. Also, we prove the existence and uniqueness of fixed point for such mappings.