Ulam–Hyers Stability and Well-Posedness of Fixed Point Problems in IC/I-Algebra Valued Bipolar Ib/I-Metric Spaces

Here, we shall introduce the new notion of C[sup.*]-algebra valued bipolar b-metric spaces as a generalization of usual metric spaces, C[sup.*]-algebra valued metric space, b-metric spaces. In the above-mentioned spaces, we shall define (α[sub.A]−ψ[sub.A]) 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.