A New Approach of Some Contractive Mappings on Metric Spaces
In this paper, we introduce a new contraction-type mapping and provide a fixed-point theorem which generalizes and improves some existing results in the literature. Thus, we prove that the Boyd and Wong theorem (1969) and, more recently, the fixed-point results due to Wardowski (2012), Turinici (201...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/12/1433 |
| _version_ | 1797529601506803712 |
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| author | Ion Marian Olaru Nicolae Adrian Secelean |
| author_facet | Ion Marian Olaru Nicolae Adrian Secelean |
| author_sort | Ion Marian Olaru |
| collection | DOAJ |
| description | In this paper, we introduce a new contraction-type mapping and provide a fixed-point theorem which generalizes and improves some existing results in the literature. Thus, we prove that the Boyd and Wong theorem (1969) and, more recently, the fixed-point results due to Wardowski (2012), Turinici (2012), Piri and Kumam (2016), Secelean (2016), Proinov (2020), and others are consequences of our main result. An application in integral equations and some illustrative examples are indicated. |
| first_indexed | 2024-03-10T10:16:03Z |
| format | Article |
| id | doaj.art-e5fbd5257c424016bd914f3c2aebe8a1 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T10:16:03Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-e5fbd5257c424016bd914f3c2aebe8a12023-11-22T00:50:44ZengMDPI AGMathematics2227-73902021-06-01912143310.3390/math9121433A New Approach of Some Contractive Mappings on Metric SpacesIon Marian Olaru0Nicolae Adrian Secelean1Department of Mathematics and Computer Science, Lucian Blaga University of Sibiu, Dr. I. Raţiu Street, No. 5–7, 550012 Sibiu, RomaniaDepartment of Mathematics and Computer Science, Lucian Blaga University of Sibiu, Dr. I. Raţiu Street, No. 5–7, 550012 Sibiu, RomaniaIn this paper, we introduce a new contraction-type mapping and provide a fixed-point theorem which generalizes and improves some existing results in the literature. Thus, we prove that the Boyd and Wong theorem (1969) and, more recently, the fixed-point results due to Wardowski (2012), Turinici (2012), Piri and Kumam (2016), Secelean (2016), Proinov (2020), and others are consequences of our main result. An application in integral equations and some illustrative examples are indicated.https://www.mdpi.com/2227-7390/9/12/1433fixed pointPicard operatorcontractive mapping |
| spellingShingle | Ion Marian Olaru Nicolae Adrian Secelean A New Approach of Some Contractive Mappings on Metric Spaces Mathematics fixed point Picard operator contractive mapping |
| title | A New Approach of Some Contractive Mappings on Metric Spaces |
| title_full | A New Approach of Some Contractive Mappings on Metric Spaces |
| title_fullStr | A New Approach of Some Contractive Mappings on Metric Spaces |
| title_full_unstemmed | A New Approach of Some Contractive Mappings on Metric Spaces |
| title_short | A New Approach of Some Contractive Mappings on Metric Spaces |
| title_sort | new approach of some contractive mappings on metric spaces |
| topic | fixed point Picard operator contractive mapping |
| url | https://www.mdpi.com/2227-7390/9/12/1433 |
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