LAHCENE, HalimaTABBAL , FairouzBouhadjera , Hakima2025-08-032025-08-032022http://dspace.univ-skikda.dz:4000/handle/123456789/5025This work consists of two parts and is focused on studying the existence and uniqueness of common fixed points for mappings satisfying weak conditions in a dislocated metric space as well as a metric space. In the first part of this work, in their paper [35], Wadkar et al. discussed the existence and uniqueness of fixed point for two pairs of weakly compatible mappings in a dislocated metric space which generalizes and improves similar fixed point results. However, this work contains a lot of mistakes in mathematics as well as in literature. The purpose of the first chapter is to repair and remedy this paper; i.e., we will correct the main result of [35] by adding some require conditions, removing certain undesirable things, rectify, change, ameliorate, modify and regulate some inevitable faults. In the second and last part, we have introduced a new concept called occasionally weakly biased mappings of type (A) in order to prove a unique common fixed point theorem for four mappings on a metric space. This theorem improves the main result of [35].enMasters degree Thesis