The purpose of this paper is to establish the uniqueness and existence of the common fixed point under generalized contractive conditions in b-metric spaces with supportive examples. We also approximate the common fixed point by Jungck-Picard and Picard iteration procedures along with the P property of the mappings. Further, (T,f)-stability of Jungck-Picard iterative and T-stability of Picard iterative schemes are proved. © 2022 World Scientific Publishing Company.