Fixed Point Theory on Triple Controlled Metric-like Spaces with a Numerical Iteration
Fixed point theory is a versatile mathematical theory that finds applications in a wide range of disciplines, including computer science, engineering, fractals, and even behavioral sciences. In this study, we propose triple controlled metric-like spaces as a generalization of controlled rectangular...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-07-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/7/1403 |
| _version_ | 1797587358439178240 |
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| author | Fatima M. Azmi Salma Haque |
| author_facet | Fatima M. Azmi Salma Haque |
| author_sort | Fatima M. Azmi |
| collection | DOAJ |
| description | Fixed point theory is a versatile mathematical theory that finds applications in a wide range of disciplines, including computer science, engineering, fractals, and even behavioral sciences. In this study, we propose triple controlled metric-like spaces as a generalization of controlled rectangular metric-like spaces. By examining the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Θ</mo></semantics></math></inline-formula>-contraction mapping within these spaces, we extend and enhance the existing literature to establish significant fixed point results. Utilizing these findings, we demonstrate the existence of solutions to a Fredholm integral equation and provide an example of a numerical iteration method applicable to a specific case of this Fredholm integral equation. |
| first_indexed | 2024-03-11T00:35:49Z |
| format | Article |
| id | doaj.art-06272597df7044e8b5bd2030e20db7d3 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T00:35:49Z |
| publishDate | 2023-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-06272597df7044e8b5bd2030e20db7d32023-11-18T21:34:34ZengMDPI AGSymmetry2073-89942023-07-01157140310.3390/sym15071403Fixed Point Theory on Triple Controlled Metric-like Spaces with a Numerical IterationFatima M. Azmi0Salma Haque1Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi ArabiaDepartment of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi ArabiaFixed point theory is a versatile mathematical theory that finds applications in a wide range of disciplines, including computer science, engineering, fractals, and even behavioral sciences. In this study, we propose triple controlled metric-like spaces as a generalization of controlled rectangular metric-like spaces. By examining the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Θ</mo></semantics></math></inline-formula>-contraction mapping within these spaces, we extend and enhance the existing literature to establish significant fixed point results. Utilizing these findings, we demonstrate the existence of solutions to a Fredholm integral equation and provide an example of a numerical iteration method applicable to a specific case of this Fredholm integral equation.https://www.mdpi.com/2073-8994/15/7/1403fixed pointtriple controlled metric like-spacesΘ-contractionFredholm integral equationcontrolled functionsnumerical iteration method |
| spellingShingle | Fatima M. Azmi Salma Haque Fixed Point Theory on Triple Controlled Metric-like Spaces with a Numerical Iteration Symmetry fixed point triple controlled metric like-spaces Θ-contraction Fredholm integral equation controlled functions numerical iteration method |
| title | Fixed Point Theory on Triple Controlled Metric-like Spaces with a Numerical Iteration |
| title_full | Fixed Point Theory on Triple Controlled Metric-like Spaces with a Numerical Iteration |
| title_fullStr | Fixed Point Theory on Triple Controlled Metric-like Spaces with a Numerical Iteration |
| title_full_unstemmed | Fixed Point Theory on Triple Controlled Metric-like Spaces with a Numerical Iteration |
| title_short | Fixed Point Theory on Triple Controlled Metric-like Spaces with a Numerical Iteration |
| title_sort | fixed point theory on triple controlled metric like spaces with a numerical iteration |
| topic | fixed point triple controlled metric like-spaces Θ-contraction Fredholm integral equation controlled functions numerical iteration method |
| url | https://www.mdpi.com/2073-8994/15/7/1403 |
| work_keys_str_mv | AT fatimamazmi fixedpointtheoryontriplecontrolledmetriclikespaceswithanumericaliteration AT salmahaque fixedpointtheoryontriplecontrolledmetriclikespaceswithanumericaliteration |