Existence and Approximation of Fixed Points of Enriched <i>φ</i>-Contractions in Banach Spaces
We introduce the class of enriched <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula>-contractions in Banach spaces as a natural generalization...
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MDPI AG
2022-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/21/4138 |
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| author | Vasile Berinde Jackie Harjani Kishin Sadarangani |
| author_facet | Vasile Berinde Jackie Harjani Kishin Sadarangani |
| author_sort | Vasile Berinde |
| collection | DOAJ |
| description | We introduce the class of enriched <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula>-contractions in Banach spaces as a natural generalization of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula>-contractions and study the existence and approximation of the fixed points of mappings in this new class, which is shown to be an unsaturated class of mappings in the setting of a Banach space. We illustrated the usefulness of our fixed point results by studying the existence and uniqueness of the solutions of some second order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-difference equations with integral boundary value conditions. |
| first_indexed | 2024-03-09T18:52:25Z |
| format | Article |
| id | doaj.art-f885f24e5cb84ea7a766ddf095933ee9 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T18:52:25Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-f885f24e5cb84ea7a766ddf095933ee92023-11-24T05:45:29ZengMDPI AGMathematics2227-73902022-11-011021413810.3390/math10214138Existence and Approximation of Fixed Points of Enriched <i>φ</i>-Contractions in Banach SpacesVasile Berinde0Jackie Harjani1Kishin Sadarangani2Department of Mathematics and Computer Science, Technical University of Baia Mare, North University Center at Baia Mare, 430122 Baia Mare, RomaniaDepartment of Mathematics, Universidad de Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, SpainDepartment of Mathematics, Universidad de Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, SpainWe introduce the class of enriched <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula>-contractions in Banach spaces as a natural generalization of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>φ</mi></semantics></math></inline-formula>-contractions and study the existence and approximation of the fixed points of mappings in this new class, which is shown to be an unsaturated class of mappings in the setting of a Banach space. We illustrated the usefulness of our fixed point results by studying the existence and uniqueness of the solutions of some second order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-difference equations with integral boundary value conditions.https://www.mdpi.com/2227-7390/10/21/4138Banach spaceenriched <i>φ</i>-contractionenriched cyclic <i>φ</i>-contractionfixed pointMaia type fixed point theorem(<i>p</i>,<i>q</i>)-difference equation |
| spellingShingle | Vasile Berinde Jackie Harjani Kishin Sadarangani Existence and Approximation of Fixed Points of Enriched <i>φ</i>-Contractions in Banach Spaces Mathematics Banach space enriched <i>φ</i>-contraction enriched cyclic <i>φ</i>-contraction fixed point Maia type fixed point theorem (<i>p</i>,<i>q</i>)-difference equation |
| title | Existence and Approximation of Fixed Points of Enriched <i>φ</i>-Contractions in Banach Spaces |
| title_full | Existence and Approximation of Fixed Points of Enriched <i>φ</i>-Contractions in Banach Spaces |
| title_fullStr | Existence and Approximation of Fixed Points of Enriched <i>φ</i>-Contractions in Banach Spaces |
| title_full_unstemmed | Existence and Approximation of Fixed Points of Enriched <i>φ</i>-Contractions in Banach Spaces |
| title_short | Existence and Approximation of Fixed Points of Enriched <i>φ</i>-Contractions in Banach Spaces |
| title_sort | existence and approximation of fixed points of enriched i φ i contractions in banach spaces |
| topic | Banach space enriched <i>φ</i>-contraction enriched cyclic <i>φ</i>-contraction fixed point Maia type fixed point theorem (<i>p</i>,<i>q</i>)-difference equation |
| url | https://www.mdpi.com/2227-7390/10/21/4138 |
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