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

Kumar M., Kumar P., MUTLU A., Ramaswamy R., Abdelnaby O. A. A., Radenović S.

Mathematics, vol.11, no.10, 2023 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 10
  • Publication Date: 2023
  • Doi Number: 10.3390/math11102323
  • Journal Name: Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: C*-algebra valued bipolar b-metric space, covariant mapping, contravariant mapping, fixed points, Ulam-Hyers stability, well-posdeness
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

Here, we shall introduce the new notion of (Formula presented.) -algebra valued bipolar b-metric spaces as a generalization of usual metric spaces, (Formula presented.) -algebra valued metric space, b-metric spaces. In the above-mentioned spaces, we shall define (Formula presented.) 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.