Analytic methods in Rhoades contractions theory (Q1982272)

In this chapter the author presents various aspects of contractive mappings defined on metric spaces. Certainly there are results of Rhoades, Boyd-Wong, Ćirić and other authors. After 2012, a significant place was taken by the \(F\)-contraction introduced by \textit{D. Wardowski} [Fixed Point Theory Appl. 2012, Paper No. 94, 6 p. (2012; Zbl 1310.54074)]. Several authors have generalized the main results of Wardowski in various ways by releasing one of the three properties of the function \(F\). In some papers, the authors assumed only a strict increase of the function \(F\). This manuscript will help many researchers to have an insight into the results achieved. For the entire collection see [Zbl 1471.34005].