Existence, Approximation and Stability of Fixed Point for Cirić Contraction in Convex <i>b</i>-Metric Spaces
We establish a new fixed point theorem in the setting of convex <i>b</i>-metric spaces that ensures the existence of fixed point for Cirić contraction with the assumption <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><...
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MDPI AG
2023-06-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/7/646 |
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| author | Gazal Savita Rathee Mahima Anshuka Kadyan Minakshi Anil Kumar |
| author_facet | Gazal Savita Rathee Mahima Anshuka Kadyan Minakshi Anil Kumar |
| author_sort | Gazal |
| collection | DOAJ |
| description | We establish a new fixed point theorem in the setting of convex <i>b</i>-metric spaces that ensures the existence of fixed point for Cirić contraction with the assumption <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo><</mo><mfrac><mn>1</mn><msup><mi>s</mi><mn>2</mn></msup></mfrac></mrow></semantics></math></inline-formula>. Also, the fixed point is approximated by Krasnoselskij iterative procedure. Moreover, we discuss the stability of fixed point for the aforesaid contraction. As a consequence, we develop a common fixed point and coincidence point result. Finally, we provide a number of examples to illustrate the findings presented here and incorporate these findings to solve an initial value problem. |
| first_indexed | 2024-03-11T01:18:14Z |
| format | Article |
| id | doaj.art-0d6331ea507143bda48549d05b0d2162 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T01:18:14Z |
| publishDate | 2023-06-01 |
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| series | Axioms |
| spelling | doaj.art-0d6331ea507143bda48549d05b0d21622023-11-18T18:17:27ZengMDPI AGAxioms2075-16802023-06-0112764610.3390/axioms12070646Existence, Approximation and Stability of Fixed Point for Cirić Contraction in Convex <i>b</i>-Metric SpacesGazal0Savita Rathee1Mahima2Anshuka Kadyan3Minakshi4Anil Kumar5Department of Engineering and Technology, Gurugram University, Gurugram 122003, Haryana, IndiaDepartment of Mathematics, Maharshi Dayanand University, Rohtak 124001, Haryana, IndiaDepartment of Engineering and Technology, Gurugram University, Gurugram 122003, Haryana, IndiaDepartment of Mathematics, Maharshi Dayanand University, Rohtak 124001, Haryana, IndiaDepartment of Mathematics, Sir Chhotu Ram Government College for Women Sampla, Rohtak 124501, Haryana, IndiaDepartment of Mathematics, Sir Chhotu Ram Government College for Women Sampla, Rohtak 124501, Haryana, IndiaWe establish a new fixed point theorem in the setting of convex <i>b</i>-metric spaces that ensures the existence of fixed point for Cirić contraction with the assumption <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo><</mo><mfrac><mn>1</mn><msup><mi>s</mi><mn>2</mn></msup></mfrac></mrow></semantics></math></inline-formula>. Also, the fixed point is approximated by Krasnoselskij iterative procedure. Moreover, we discuss the stability of fixed point for the aforesaid contraction. As a consequence, we develop a common fixed point and coincidence point result. Finally, we provide a number of examples to illustrate the findings presented here and incorporate these findings to solve an initial value problem.https://www.mdpi.com/2075-1680/12/7/646<i>b</i>-metric spacesconvex metric spacesapproximationstabilitycirić contraction |
| spellingShingle | Gazal Savita Rathee Mahima Anshuka Kadyan Minakshi Anil Kumar Existence, Approximation and Stability of Fixed Point for Cirić Contraction in Convex <i>b</i>-Metric Spaces Axioms <i>b</i>-metric spaces convex metric spaces approximation stability cirić contraction |
| title | Existence, Approximation and Stability of Fixed Point for Cirić Contraction in Convex <i>b</i>-Metric Spaces |
| title_full | Existence, Approximation and Stability of Fixed Point for Cirić Contraction in Convex <i>b</i>-Metric Spaces |
| title_fullStr | Existence, Approximation and Stability of Fixed Point for Cirić Contraction in Convex <i>b</i>-Metric Spaces |
| title_full_unstemmed | Existence, Approximation and Stability of Fixed Point for Cirić Contraction in Convex <i>b</i>-Metric Spaces |
| title_short | Existence, Approximation and Stability of Fixed Point for Cirić Contraction in Convex <i>b</i>-Metric Spaces |
| title_sort | existence approximation and stability of fixed point for ciric contraction in convex i b i metric spaces |
| topic | <i>b</i>-metric spaces convex metric spaces approximation stability cirić contraction |
| url | https://www.mdpi.com/2075-1680/12/7/646 |
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