Ample Spectrum Contractions and Related Fixed Point Theorems
Simulation functions were introduced by Khojasteh et al. as a method to extend several classes of fixed point theorems by a simple condition. After that, many researchers have amplified the knowledge of such kind of contractions in several ways. <i>R</i>-functions, <inline-formula>...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/7/11/1033 |
| _version_ | 1819113323200774144 |
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| author | Antonio Francisco Roldán López de Hierro Naseer Shahzad |
| author_facet | Antonio Francisco Roldán López de Hierro Naseer Shahzad |
| author_sort | Antonio Francisco Roldán López de Hierro |
| collection | DOAJ |
| description | Simulation functions were introduced by Khojasteh et al. as a method to extend several classes of fixed point theorems by a simple condition. After that, many researchers have amplified the knowledge of such kind of contractions in several ways. <i>R</i>-functions, <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>R</mi> <mo>,</mo> <mi mathvariant="script">S</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-contractions and <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi mathvariant="script">A</mi> <mo>,</mo> <mi mathvariant="script">S</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-contractions can be considered as approaches in this direction. A common characteristic of the previous kind of contractive maps is the fact that they are defined by a strict inequality. In this manuscript, we show the advantages of replacing such inequality with a weaker one, involving a family of more general auxiliary functions. As a consequence of our study, we show that not only the above-commented contractions are particular cases, but also another classes of contractive maps correspond to this new point of view. |
| first_indexed | 2024-12-22T04:27:34Z |
| format | Article |
| id | doaj.art-de278b89bf7245b08b82422b6e319a94 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-22T04:27:34Z |
| publishDate | 2019-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-de278b89bf7245b08b82422b6e319a942022-12-21T18:39:07ZengMDPI AGMathematics2227-73902019-11-01711103310.3390/math7111033math7111033Ample Spectrum Contractions and Related Fixed Point TheoremsAntonio Francisco Roldán López de Hierro0Naseer Shahzad1Department of Statistics and Operations Research, University of Granada, Granada 18010, SpainDepartment of Mathematics, Faculty of Science, King Abdulaziz University, P.O.B. 80203, Jeddah 21589, Saudi ArabiaSimulation functions were introduced by Khojasteh et al. as a method to extend several classes of fixed point theorems by a simple condition. After that, many researchers have amplified the knowledge of such kind of contractions in several ways. <i>R</i>-functions, <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>R</mi> <mo>,</mo> <mi mathvariant="script">S</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-contractions and <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi mathvariant="script">A</mi> <mo>,</mo> <mi mathvariant="script">S</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-contractions can be considered as approaches in this direction. A common characteristic of the previous kind of contractive maps is the fact that they are defined by a strict inequality. In this manuscript, we show the advantages of replacing such inequality with a weaker one, involving a family of more general auxiliary functions. As a consequence of our study, we show that not only the above-commented contractions are particular cases, but also another classes of contractive maps correspond to this new point of view.https://www.mdpi.com/2227-7390/7/11/1033r-functionsimulation functionmanageable functionfixed pointcontractivity conditionbinary relation |
| spellingShingle | Antonio Francisco Roldán López de Hierro Naseer Shahzad Ample Spectrum Contractions and Related Fixed Point Theorems Mathematics r-function simulation function manageable function fixed point contractivity condition binary relation |
| title | Ample Spectrum Contractions and Related Fixed Point Theorems |
| title_full | Ample Spectrum Contractions and Related Fixed Point Theorems |
| title_fullStr | Ample Spectrum Contractions and Related Fixed Point Theorems |
| title_full_unstemmed | Ample Spectrum Contractions and Related Fixed Point Theorems |
| title_short | Ample Spectrum Contractions and Related Fixed Point Theorems |
| title_sort | ample spectrum contractions and related fixed point theorems |
| topic | r-function simulation function manageable function fixed point contractivity condition binary relation |
| url | https://www.mdpi.com/2227-7390/7/11/1033 |
| work_keys_str_mv | AT antoniofranciscoroldanlopezdehierro amplespectrumcontractionsandrelatedfixedpointtheorems AT naseershahzad amplespectrumcontractionsandrelatedfixedpointtheorems |