Solving Integral Equation and Homotopy Result via Fixed Point Method
The aim of the present research article is to investigate the existence and uniqueness of a solution to the integral equation and homotopy result. To achieve our objective, we introduce the notion of (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="i...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/21/4408 |
| _version_ | 1827765605203181568 |
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| author | Badriah Alamri |
| author_facet | Badriah Alamri |
| author_sort | Badriah Alamri |
| collection | DOAJ |
| description | The aim of the present research article is to investigate the existence and uniqueness of a solution to the integral equation and homotopy result. To achieve our objective, we introduce the notion of (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>,</mo><mi>η</mi><mo>,</mo><mi>ψ</mi></mrow></semantics></math></inline-formula>)-contraction in the framework of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">F</mi></semantics></math></inline-formula>-bipolar metric space and prove some fixed point results for covariant and contravariant mappings. Some coupled fixed point results in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">F</mi></semantics></math></inline-formula>-bipolar metric space are derived as outcomes of our principal theorems. A non-trivial example is also provided to validate the authenticity of the established results. |
| first_indexed | 2024-03-11T11:24:57Z |
| format | Article |
| id | doaj.art-05ce771acbc449aab368b3bfac704b95 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T11:24:57Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-05ce771acbc449aab368b3bfac704b952023-11-10T15:07:47ZengMDPI AGMathematics2227-73902023-10-011121440810.3390/math11214408Solving Integral Equation and Homotopy Result via Fixed Point MethodBadriah Alamri0Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah 23218, Saudi ArabiaThe aim of the present research article is to investigate the existence and uniqueness of a solution to the integral equation and homotopy result. To achieve our objective, we introduce the notion of (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>,</mo><mi>η</mi><mo>,</mo><mi>ψ</mi></mrow></semantics></math></inline-formula>)-contraction in the framework of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">F</mi></semantics></math></inline-formula>-bipolar metric space and prove some fixed point results for covariant and contravariant mappings. Some coupled fixed point results in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">F</mi></semantics></math></inline-formula>-bipolar metric space are derived as outcomes of our principal theorems. A non-trivial example is also provided to validate the authenticity of the established results.https://www.mdpi.com/2227-7390/11/21/4408fixed pointgeneralized contractions<i>?</i>-bipolar metric spaceintegral equationhomotopy |
| spellingShingle | Badriah Alamri Solving Integral Equation and Homotopy Result via Fixed Point Method Mathematics fixed point generalized contractions <i>?</i>-bipolar metric space integral equation homotopy |
| title | Solving Integral Equation and Homotopy Result via Fixed Point Method |
| title_full | Solving Integral Equation and Homotopy Result via Fixed Point Method |
| title_fullStr | Solving Integral Equation and Homotopy Result via Fixed Point Method |
| title_full_unstemmed | Solving Integral Equation and Homotopy Result via Fixed Point Method |
| title_short | Solving Integral Equation and Homotopy Result via Fixed Point Method |
| title_sort | solving integral equation and homotopy result via fixed point method |
| topic | fixed point generalized contractions <i>?</i>-bipolar metric space integral equation homotopy |
| url | https://www.mdpi.com/2227-7390/11/21/4408 |
| work_keys_str_mv | AT badriahalamri solvingintegralequationandhomotopyresultviafixedpointmethod |