The extendibility of the Banach iteration technique to some contraction mappings with variations in partial metric space domains to establish some fixed-point results has been discussed in this article. A map that satisfies the contraction condition has been proposed for an increasing sequence of subsets of a partial metric space, where one element of the sequence is mapped into the following member of the sequence. Additionally, some fixed-point theorems are established for contraction mappings of Banach, Kannan, Chatterjee, and Hardy–Roger types with closed graphs.