Ulam–Hyers Stability and Well-Posedness of Fixed Point Problems in C*-Algebra Valued Bipolar b-Metric Spaces

Abstract

Here, we shall introduce the new notion of C*-algebra valued bipolar b-metric spaces as a generalization of usual metric spaces, C*-algebra valued metric space, b-metric spaces. In the above-mentioned spaces, we shall define (αA−ψA) contractions and prove some fixed point theorems for these contractions. Some existing results from the literature are also proved by using our main results. As an application Ulam–Hyers stability and well-posedness of fixed point problems are also discussed. Some examples are also given to illustrate our results.