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

Kumar, Manoj; Kumar, Pankaj; Mutlu, Ali; Ramaswamy, Rajagopalan; Abdelnaby, Ola A. Ashour; Radenović, Stojan

doi:10.3390/math11102323

Open AccessArticle

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

by

Manoj Kumar

¹

,

Pankaj Kumar

¹,

Ali Mutlu

²,

Rajagopalan Ramaswamy

^3,*

,

Ola A. Ashour Abdelnaby

^3,4 and

Stojan Radenović

⁵

¹

Department of Mathematics, Baba Mastnath University, Asthal Bohar, Rohtak 124021, Haryana, India

²

Department of Mathematics, Faculty of Science and Arts, Manisa Celal Bayar University, Martyr Prof. Dr. İlhan Varank Campus, 45140 Manisa, Türkiye

³

Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, AlKharj 11942, Saudi Arabia

⁴

Department of Mathematics, Cairo University, Cairo 12613, Egypt

⁵

Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, Serbia

^*

Author to whom correspondence should be addressed.

Mathematics 2023, 11(10), 2323; https://doi.org/10.3390/math11102323

Submission received: 25 February 2023 / Revised: 3 April 2023 / Accepted: 21 April 2023 / Published: 16 May 2023

(This article belongs to the Special Issue New Advances in Fuzzy Metric Spaces, Soft Metric Spaces, and Other Related Structures, 2nd Edition)

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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

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MDPI and ACS Style

Kumar, M.; Kumar, P.; Mutlu, A.; Ramaswamy, R.; Abdelnaby, O.A.A.; Radenović, S. Ulam–Hyers Stability and Well-Posedness of Fixed Point Problems in C*-Algebra Valued Bipolar b-Metric Spaces. Mathematics 2023, 11, 2323. https://doi.org/10.3390/math11102323

AMA Style

Kumar M, Kumar P, Mutlu A, Ramaswamy R, Abdelnaby OAA, Radenović S. Ulam–Hyers Stability and Well-Posedness of Fixed Point Problems in C*-Algebra Valued Bipolar b-Metric Spaces. Mathematics. 2023; 11(10):2323. https://doi.org/10.3390/math11102323

Chicago/Turabian Style

Kumar, Manoj, Pankaj Kumar, Ali Mutlu, Rajagopalan Ramaswamy, Ola A. Ashour Abdelnaby, and Stojan Radenović. 2023. "Ulam–Hyers Stability and Well-Posedness of Fixed Point Problems in C*-Algebra Valued Bipolar b-Metric Spaces" Mathematics 11, no. 10: 2323. https://doi.org/10.3390/math11102323

APA Style

Kumar, M., Kumar, P., Mutlu, A., Ramaswamy, R., Abdelnaby, O. A. A., & Radenović, S. (2023). Ulam–Hyers Stability and Well-Posedness of Fixed Point Problems in C*-Algebra Valued Bipolar b-Metric Spaces. Mathematics, 11(10), 2323. https://doi.org/10.3390/math11102323

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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

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