The convergence of generalized pseudo-contractive operators were studied with regard to a unique fixed point in the article (Verma in Proc Roy Irish Acad Soct A, 97(1):83–86, 1997). In this present article, we introduce Jungck generalized pseudo-contractive and Lipschitzian type operators in the prehilbertian space and in the Hilbert space settings, establish the existence and the uniqueness of a common fixed point for the operator S and a sequence of operators $$\{T_i:D\rightarrow D\}_{i=1}^k$$ { T i : D → D } i = 1 k using a new Jungck–Kirk–Mann type fixed point iterative algorithm as well as the general Kirk–Mann type iterative algorithm. The strong convergence of these fixed point iterative algorithms to a unique common fixed point is also investigated for the same set of operators considered. Moreover, some stability results are established for the Jungck–Kirk–Mann type iterative algorithm as well as the general Kirk–Mann type iterative algorithm. In addition, some examples are given to support our arguments. The results are new, original as well as generalizing some existing ones in the literature.