Fixed point results and application for cyclic contractive maps in b-metric spaces
One of the generalizations of the usual metric function is b-metric, which allows the researchers a wider aria to derive many results and applications regarding the fixed point theory. This aim of the article is to advance new three fixed point principles in complete b-metric space instance is c...
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University of Baghdad
2025-04-01
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| Series: | Ibn Al-Haitham Journal for Pure and Applied Sciences |
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| Online Access: | https://jih.uobaghdad.edu.iq/index.php/j/article/view/3828 |
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| author | Abbas Karim Nahi Salwa Salman Abed |
| author_facet | Abbas Karim Nahi Salwa Salman Abed |
| author_sort | Abbas Karim Nahi |
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One of the generalizations of the usual metric function is b-metric, which allows the researchers a wider aria to derive many results and applications regarding the fixed point theory. This aim of the article is to advance new three fixed point principles in complete b-metric space instance is continuous function in two variables. Here, there are three directions to prove existence and uniqueness of fixed point. First, deriving a result in sense of Branciari’s theorem by combining integral contractive conditions with the idea of cyclic map. Second, applying the notion of cyclic representation regarding maps satisfying general weak conditions including an altering distance function to simulate the content of Boyd and Wong theorem. By this result, an application is given about the existence and uniqueness solution of an integral equation. Lastly, using an implicit relation with an altering distance function to construct cyclic contractive map. Furthermore, some examples are presented to analyze and illustrate the main results.
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| format | Article |
| id | doaj-art-9e8dac9d3d7a4255ab22b8cf5f0218c5 |
| institution | OA Journals |
| issn | 1609-4042 2521-3407 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | University of Baghdad |
| record_format | Article |
| series | Ibn Al-Haitham Journal for Pure and Applied Sciences |
| spelling | doaj-art-9e8dac9d3d7a4255ab22b8cf5f0218c52025-08-20T02:12:15ZengUniversity of BaghdadIbn Al-Haitham Journal for Pure and Applied Sciences1609-40422521-34072025-04-0138210.30526/38.2.3828Fixed point results and application for cyclic contractive maps in b-metric spacesAbbas Karim Nahi0https://orcid.org/0009-0006-3158-1348Salwa Salman Abed1https://orcid.org/0000-0002-0581-253XDepartment of Mathematics, College of Education for Pure Science (Ibn Al-Haitham), University of Baghdad, Baghdad, IraqDepartment of Mathematics, College of Education for Pure Science (Ibn Al-Haitham), University of Baghdad, Baghdad, Iraq. One of the generalizations of the usual metric function is b-metric, which allows the researchers a wider aria to derive many results and applications regarding the fixed point theory. This aim of the article is to advance new three fixed point principles in complete b-metric space instance is continuous function in two variables. Here, there are three directions to prove existence and uniqueness of fixed point. First, deriving a result in sense of Branciari’s theorem by combining integral contractive conditions with the idea of cyclic map. Second, applying the notion of cyclic representation regarding maps satisfying general weak conditions including an altering distance function to simulate the content of Boyd and Wong theorem. By this result, an application is given about the existence and uniqueness solution of an integral equation. Lastly, using an implicit relation with an altering distance function to construct cyclic contractive map. Furthermore, some examples are presented to analyze and illustrate the main results. https://jih.uobaghdad.edu.iq/index.php/j/article/view/3828Altering distance functions, Complete b-metric spaces, Contractive conditions, Cyclic representation, Fixed points |
| spellingShingle | Abbas Karim Nahi Salwa Salman Abed Fixed point results and application for cyclic contractive maps in b-metric spaces Ibn Al-Haitham Journal for Pure and Applied Sciences Altering distance functions, Complete b-metric spaces, Contractive conditions, Cyclic representation, Fixed points |
| title | Fixed point results and application for cyclic contractive maps in b-metric spaces |
| title_full | Fixed point results and application for cyclic contractive maps in b-metric spaces |
| title_fullStr | Fixed point results and application for cyclic contractive maps in b-metric spaces |
| title_full_unstemmed | Fixed point results and application for cyclic contractive maps in b-metric spaces |
| title_short | Fixed point results and application for cyclic contractive maps in b-metric spaces |
| title_sort | fixed point results and application for cyclic contractive maps in b metric spaces |
| topic | Altering distance functions, Complete b-metric spaces, Contractive conditions, Cyclic representation, Fixed points |
| url | https://jih.uobaghdad.edu.iq/index.php/j/article/view/3828 |
| work_keys_str_mv | AT abbaskarimnahi fixedpointresultsandapplicationforcycliccontractivemapsinbmetricspaces AT salwasalmanabed fixedpointresultsandapplicationforcycliccontractivemapsinbmetricspaces |