Ulam–Hyers Stability and Well-Posedness of Fixed Point Problems in <i>C</i>*-Algebra Valued Bipolar <i>b</i>-Metric Spaces
Here, we shall introduce the new notion of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>C</mi><mo>*</mo></msup></semantics></math></inline-formula>-al...
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MDPI AG
2023-05-01
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| author | Manoj Kumar Pankaj Kumar Ali Mutlu Rajagopalan Ramaswamy Ola A. Ashour Abdelnaby Stojan Radenović |
| author_facet | Manoj Kumar Pankaj Kumar Ali Mutlu Rajagopalan Ramaswamy Ola A. Ashour Abdelnaby Stojan Radenović |
| author_sort | Manoj Kumar |
| collection | DOAJ |
| description | Here, we shall introduce the new notion of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>C</mi><mo>*</mo></msup></semantics></math></inline-formula>-algebra valued bipolar <i>b</i>-metric spaces as a generalization of usual metric spaces, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>C</mi><mo>*</mo></msup></semantics></math></inline-formula>-algebra valued metric space, <i>b</i>-metric spaces. In the above-mentioned spaces, we shall define <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi>α</mi><mi mathvariant="fraktur">A</mi></msub><mo>−</mo><msub><mi>ψ</mi><mi mathvariant="fraktur">A</mi></msub><mo>)</mo></mrow></semantics></math></inline-formula> 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. |
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| language | English |
| last_indexed | 2024-03-11T03:31:43Z |
| publishDate | 2023-05-01 |
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| spelling | doaj.art-da52824da9eb40ae9677a61b66508fb22023-11-18T02:19:19ZengMDPI AGMathematics2227-73902023-05-011110232310.3390/math11102323Ulam–Hyers Stability and Well-Posedness of Fixed Point Problems in <i>C</i>*-Algebra Valued Bipolar <i>b</i>-Metric SpacesManoj Kumar0Pankaj Kumar1Ali Mutlu2Rajagopalan Ramaswamy3Ola A. Ashour Abdelnaby4Stojan Radenović5Department of Mathematics, Baba Mastnath University, Asthal Bohar, Rohtak 124021, Haryana, IndiaDepartment of Mathematics, Baba Mastnath University, Asthal Bohar, Rohtak 124021, Haryana, IndiaDepartment of Mathematics, Faculty of Science and Arts, Manisa Celal Bayar University, Martyr Prof. Dr. İlhan Varank Campus, 45140 Manisa, TürkiyeDepartment of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, AlKharj 11942, Saudi ArabiaDepartment of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, AlKharj 11942, Saudi ArabiaFaculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, SerbiaHere, we shall introduce the new notion of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>C</mi><mo>*</mo></msup></semantics></math></inline-formula>-algebra valued bipolar <i>b</i>-metric spaces as a generalization of usual metric spaces, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>C</mi><mo>*</mo></msup></semantics></math></inline-formula>-algebra valued metric space, <i>b</i>-metric spaces. In the above-mentioned spaces, we shall define <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi>α</mi><mi mathvariant="fraktur">A</mi></msub><mo>−</mo><msub><mi>ψ</mi><mi mathvariant="fraktur">A</mi></msub><mo>)</mo></mrow></semantics></math></inline-formula> 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.https://www.mdpi.com/2227-7390/11/10/2323<i>C</i>*-algebra valued bipolar <i>b</i>-metric spacecovariant mappingcontravariant mappingfixed pointsUlam–Hyers stabilitywell-posdeness |
| spellingShingle | Manoj Kumar Pankaj Kumar Ali Mutlu Rajagopalan Ramaswamy Ola A. Ashour Abdelnaby Stojan Radenović Ulam–Hyers Stability and Well-Posedness of Fixed Point Problems in <i>C</i>*-Algebra Valued Bipolar <i>b</i>-Metric Spaces Mathematics <i>C</i>*-algebra valued bipolar <i>b</i>-metric space covariant mapping contravariant mapping fixed points Ulam–Hyers stability well-posdeness |
| title | Ulam–Hyers Stability and Well-Posedness of Fixed Point Problems in <i>C</i>*-Algebra Valued Bipolar <i>b</i>-Metric Spaces |
| title_full | Ulam–Hyers Stability and Well-Posedness of Fixed Point Problems in <i>C</i>*-Algebra Valued Bipolar <i>b</i>-Metric Spaces |
| title_fullStr | Ulam–Hyers Stability and Well-Posedness of Fixed Point Problems in <i>C</i>*-Algebra Valued Bipolar <i>b</i>-Metric Spaces |
| title_full_unstemmed | Ulam–Hyers Stability and Well-Posedness of Fixed Point Problems in <i>C</i>*-Algebra Valued Bipolar <i>b</i>-Metric Spaces |
| title_short | Ulam–Hyers Stability and Well-Posedness of Fixed Point Problems in <i>C</i>*-Algebra Valued Bipolar <i>b</i>-Metric Spaces |
| title_sort | ulam hyers stability and well posedness of fixed point problems in i c i algebra valued bipolar i b i metric spaces |
| topic | <i>C</i>*-algebra valued bipolar <i>b</i>-metric space covariant mapping contravariant mapping fixed points Ulam–Hyers stability well-posdeness |
| url | https://www.mdpi.com/2227-7390/11/10/2323 |
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