Fixed Point of (<i>α</i>,<i>β</i>)-Admissible Generalized Geraghty <i>F</i>-Contraction with Application
In this paper, we introduce some new types of extended Geraghty contractions, called <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>α</mi><mo>,</mo><mi...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-05-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/5/1016 |
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| author | Min Wang Naeem Saleem Xiaolan Liu Arslan Hojat Ansari Mi Zhou |
| author_facet | Min Wang Naeem Saleem Xiaolan Liu Arslan Hojat Ansari Mi Zhou |
| author_sort | Min Wang |
| collection | DOAJ |
| description | In this paper, we introduce some new types of extended Geraghty contractions, called <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>)</mo></mrow></semantics></math></inline-formula>-admissible generalized Geraghty <i>F</i>-contractions, and prove some fixed point results for such contractions in the setting of partial <i>b</i>-metric spaces. Moreover, based on the obtained fixed point results and the property of symmetry, we inaugurate a fixed point result for graphic generalized Geraghty <i>F</i>-contractions defined on partial metric spaces endowed with a directed graph. As an application, we examine the existence of a unique solution to the first-order periodic boundary value by the obtained fixed point result. Moreover, some examples are presented to illustrate the validity of the new results. |
| first_indexed | 2024-03-10T01:43:48Z |
| format | Article |
| id | doaj.art-f84524e0cf4a4baaab190eeb535c7ffb |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T01:43:48Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-f84524e0cf4a4baaab190eeb535c7ffb2023-11-23T13:20:02ZengMDPI AGSymmetry2073-89942022-05-01145101610.3390/sym14051016Fixed Point of (<i>α</i>,<i>β</i>)-Admissible Generalized Geraghty <i>F</i>-Contraction with ApplicationMin Wang0Naeem Saleem1Xiaolan Liu2Arslan Hojat Ansari3Mi Zhou4School of Science and Physics, Mianyang Teachers’ College, Mianyang 621000, ChinaDepartment of Mathematics, University of Management and Technology, Lahore 54770, PakistanCollege of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, ChinaDepartment of Mathematics, Karaj Brancem Islamic Azad University, Karaj 61349-37333, IranSchool of Science and Technology, Sanya University, Sanya 572000, ChinaIn this paper, we introduce some new types of extended Geraghty contractions, called <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>)</mo></mrow></semantics></math></inline-formula>-admissible generalized Geraghty <i>F</i>-contractions, and prove some fixed point results for such contractions in the setting of partial <i>b</i>-metric spaces. Moreover, based on the obtained fixed point results and the property of symmetry, we inaugurate a fixed point result for graphic generalized Geraghty <i>F</i>-contractions defined on partial metric spaces endowed with a directed graph. As an application, we examine the existence of a unique solution to the first-order periodic boundary value by the obtained fixed point result. Moreover, some examples are presented to illustrate the validity of the new results.https://www.mdpi.com/2073-8994/14/5/1016fixed pointpartial metric spaces<i>b</i>-metric spaces<i>F</i>-contraction(<i>α</i>,<i>β</i>)-admissible |
| spellingShingle | Min Wang Naeem Saleem Xiaolan Liu Arslan Hojat Ansari Mi Zhou Fixed Point of (<i>α</i>,<i>β</i>)-Admissible Generalized Geraghty <i>F</i>-Contraction with Application Symmetry fixed point partial metric spaces <i>b</i>-metric spaces <i>F</i>-contraction (<i>α</i>,<i>β</i>)-admissible |
| title | Fixed Point of (<i>α</i>,<i>β</i>)-Admissible Generalized Geraghty <i>F</i>-Contraction with Application |
| title_full | Fixed Point of (<i>α</i>,<i>β</i>)-Admissible Generalized Geraghty <i>F</i>-Contraction with Application |
| title_fullStr | Fixed Point of (<i>α</i>,<i>β</i>)-Admissible Generalized Geraghty <i>F</i>-Contraction with Application |
| title_full_unstemmed | Fixed Point of (<i>α</i>,<i>β</i>)-Admissible Generalized Geraghty <i>F</i>-Contraction with Application |
| title_short | Fixed Point of (<i>α</i>,<i>β</i>)-Admissible Generalized Geraghty <i>F</i>-Contraction with Application |
| title_sort | fixed point of i α i i β i admissible generalized geraghty i f i contraction with application |
| topic | fixed point partial metric spaces <i>b</i>-metric spaces <i>F</i>-contraction (<i>α</i>,<i>β</i>)-admissible |
| url | https://www.mdpi.com/2073-8994/14/5/1016 |
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