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

Manoj Kumar, Pankaj Kumar, Ali Mutlu, Rajagopalan Ramaswamy (), Ola A. Ashour Abdelnaby and Stojan Radenović
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Manoj Kumar: Department of Mathematics, Baba Mastnath University, Asthal Bohar, Rohtak 124021, Haryana, India
Pankaj Kumar: Department of Mathematics, Baba Mastnath University, Asthal Bohar, Rohtak 124021, Haryana, India
Ali Mutlu: Department of Mathematics, Faculty of Science and Arts, Manisa Celal Bayar University, Martyr Prof. Dr. İlhan Varank Campus, 45140 Manisa, Türkiye
Rajagopalan Ramaswamy: Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, AlKharj 11942, Saudi Arabia
Ola A. Ashour Abdelnaby: Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, AlKharj 11942, Saudi Arabia
Stojan Radenović: Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, Serbia

Mathematics, 2023, vol. 11, issue 10, 1-14

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 ( α A − ψ 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.

Keywords: C *-algebra valued bipolar b -metric space; covariant mapping; contravariant mapping; fixed points; Ulam–Hyers stability; well-posdeness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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