Korean J. Math. Vol. 34 No. 3 (2026) pp.437-448
DOI: https://doi.org/10.11568/kjm.2026.34.3.437

Some fixed point results in $C^{\ast}$-algebra valued bipolar $b-$metric spaces

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Published: Sep 30, 2026
Keywords:
Fixed point, $C^{\ast}$-algebra valued metric spaces, $C^{\ast}$-algebra valued bipolar $b$-metric spaces
Mathematics Subject Classification:
41A58, 42C15, 46L05

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Maryam Alshehri
Department of Mathematics, Faculty of Science, University of Tabuk, P.O.Box 741, Tabuk 71491, Saudi Arabia
Hafida Massit
Laboratory Analysis, Geometry and Applications, Faculty of Science, University of Ibn Tofail, P.O. Box 133, Kenitra 14000, Morocco
Mohamed Rossafi
Laboratory Analysis, Geometry and Applications, Higher School of Education and Training, University of Ibn Tofail, P. O. Box 242, Kenitra 14000, Morocco
Zoran Mitrovic ́
Faculty of Electrical Engineering, University of Banja Luka, Patre 5, 78000 Banja Luka, Bosnia and Herzegovina

Abstract




In this paper, we prove the existence and uniqueness of fixed point and common fixed point under Banach and Kannan type contractions in the setting of $C^{\ast}$-algebra valued bipolar $b$-metric spaces. Further, few examples are given to justify the findings. Our results improve and generalize some results from the literature, at the end we give several open problems.






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