University of MaraghehSahand Communications in Mathematical Analysis2322-580716120191001Generalized $F$-contractions in Partially Ordered Metric Spaces931043605910.22130/scma.2018.81871.398ENSeyede Samira RazaviFaculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran.Hashem Parvaneh MasihaFaculty of Mathematics, K. N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran.Journal Article20180220We discuss about the generalized $F$-contraction mappings in partially ordered metric spaces. For this, we first introduce the notion of ordered weakly $F$-contraction mapping. We also present some fixed point results about this type of mapping in partially ordered metric spaces. Next, we introduce the notion of $acute{mathrm{C}}$iri$acute{mathrm{c}}$ type generalized ordered weakly $F$-contraction mapping. We also prove some fixed point results about this notion in partially ordered metric spaces. We also provide an example to support our results. In fact, this example shows that our main theorem is a genuine generalization in the area of the generalized $F$-contraction mappings in partially ordered metric spaces.http://scma.maragheh.ac.ir/article_36059_bd5685c96b785d3676909c2ba3cf34a2.pdf