Keywords: relational metric space; fixed point; Picard operator; Cauchy/convergent sequence; implicit analytic method; Rhoades contraction; regulated function

Review Text: In this chapter the author presents various aspects of contractive mappings defined on metric space. 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 Wardowski. Several authors have generalized main result of Wardovski in various ways by releasing one of the three properties of function F. In some papers, the authors assumed only a strict increase of the function of F. This manuscript will help many researchers to have an insight into the results achieved.