Basic Contractions of Suzuki-Type on Quasi-Metric Spaces and Fixed Point Results
This paper deals with the question of achieving a suitable extension of the notion of Suzuki-type contraction to the framework of quasi-metric spaces, which allows us to obtain reasonable fixed point theorems in the quasi-metric context. This question has no an easy answer; in fact, we here present...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/21/3931 |
| _version_ | 1797467400934785024 |
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| author | Salvador Romaguera |
| author_facet | Salvador Romaguera |
| author_sort | Salvador Romaguera |
| collection | DOAJ |
| description | This paper deals with the question of achieving a suitable extension of the notion of Suzuki-type contraction to the framework of quasi-metric spaces, which allows us to obtain reasonable fixed point theorems in the quasi-metric context. This question has no an easy answer; in fact, we here present an example of a self map of Smyth complete quasi-metric space (a very strong kind of quasi-metric completeness) that fulfills a simple and natural contraction of Suzuki-type but does not have fixed points. Despite it, we implement an approach to obtain two fixed point results, whose validity is supported with several examples. Finally, we present a general method to construct non-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mn>1</mn></msub></semantics></math></inline-formula> quasi-metric spaces in such a way that it is possible to systematically generate non-Banach contractions which are of Suzuki-type. Thus, we can apply our results to deduce the existence and uniqueness of solution for some kinds of functional equations which is exemplified with a distinguished case. |
| first_indexed | 2024-03-09T18:53:07Z |
| format | Article |
| id | doaj.art-aa01b4dbc01a485e94d52138b3f8b590 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T18:53:07Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-aa01b4dbc01a485e94d52138b3f8b5902023-11-24T05:42:16ZengMDPI AGMathematics2227-73902022-10-011021393110.3390/math10213931Basic Contractions of Suzuki-Type on Quasi-Metric Spaces and Fixed Point ResultsSalvador Romaguera0Instituto Universitario de Matemática Pura y Aplicada-IUMPA, Universitat Politècnica de València, 46022 Valencia, SpainThis paper deals with the question of achieving a suitable extension of the notion of Suzuki-type contraction to the framework of quasi-metric spaces, which allows us to obtain reasonable fixed point theorems in the quasi-metric context. This question has no an easy answer; in fact, we here present an example of a self map of Smyth complete quasi-metric space (a very strong kind of quasi-metric completeness) that fulfills a simple and natural contraction of Suzuki-type but does not have fixed points. Despite it, we implement an approach to obtain two fixed point results, whose validity is supported with several examples. Finally, we present a general method to construct non-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mn>1</mn></msub></semantics></math></inline-formula> quasi-metric spaces in such a way that it is possible to systematically generate non-Banach contractions which are of Suzuki-type. Thus, we can apply our results to deduce the existence and uniqueness of solution for some kinds of functional equations which is exemplified with a distinguished case.https://www.mdpi.com/2227-7390/10/21/3931contraction of Suzuki-typefixed pointquasi-metriccomplete |
| spellingShingle | Salvador Romaguera Basic Contractions of Suzuki-Type on Quasi-Metric Spaces and Fixed Point Results Mathematics contraction of Suzuki-type fixed point quasi-metric complete |
| title | Basic Contractions of Suzuki-Type on Quasi-Metric Spaces and Fixed Point Results |
| title_full | Basic Contractions of Suzuki-Type on Quasi-Metric Spaces and Fixed Point Results |
| title_fullStr | Basic Contractions of Suzuki-Type on Quasi-Metric Spaces and Fixed Point Results |
| title_full_unstemmed | Basic Contractions of Suzuki-Type on Quasi-Metric Spaces and Fixed Point Results |
| title_short | Basic Contractions of Suzuki-Type on Quasi-Metric Spaces and Fixed Point Results |
| title_sort | basic contractions of suzuki type on quasi metric spaces and fixed point results |
| topic | contraction of Suzuki-type fixed point quasi-metric complete |
| url | https://www.mdpi.com/2227-7390/10/21/3931 |
| work_keys_str_mv | AT salvadorromaguera basiccontractionsofsuzukitypeonquasimetricspacesandfixedpointresults |