Quasi-contraction operators with common fixed point results and applications to stability, well-posedness Ostrowski property

The purpose of this paper is to present some common fixed point results for two quasi-contraction operators in complete metric space which provide a positive answer to the question of Mihiţ, Moţ and Petruşel [16], concerning common fixed point results. Here we have established the existence and uniqueness of the common fixed point results to apply in stability analysis. More precisely, we will also see under which conditions the common fixed point problem satisfies well-posedness, Ulam-Hyers stability, and Ostrowski’s property. Illustrative examples and an application are given to support the obtained results, which extend some of the theorems in the recent literature.