Certain Fixed-Point Results for (<inline-formula><math display="inline"><semantics><mrow><mi mathvariant="fraktur">e</mi></mrow></semantics></math></inline-formula>,<i>ψ</i>,Φ)-Enriched Weak Contractions via Theoretic Order with Applications
This paper aims to establish several fixed-point theorems within the framework of Banach spaces endowed with a binary relation. By utilizing enriched contraction principles involving two classes of altering-distance functions, the study encompasses various types of contractive mappings, including th...
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2025-02-01
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| author | Umar Ishtiaq Muhammad Din Yumnam Rohen Khalid A. Alnowibet Ioan-Lucian Popa |
| author_facet | Umar Ishtiaq Muhammad Din Yumnam Rohen Khalid A. Alnowibet Ioan-Lucian Popa |
| author_sort | Umar Ishtiaq |
| collection | DOAJ |
| description | This paper aims to establish several fixed-point theorems within the framework of Banach spaces endowed with a binary relation. By utilizing enriched contraction principles involving two classes of altering-distance functions, the study encompasses various types of contractive mappings, including theoretic-order contractions, Picard–Banach contractions, weak contractions, and non-expansive contractions. A suitable Krasnoselskij iterative scheme is employed to derive the results. Many well-known fixed-point theorems (FPTs) can be obtained as special cases of these findings by assigning specific control functions in the main definitions or selecting an appropriate binary relation. To validate the theoretical results, numerous illustrative examples are provided. Furthermore, the paper demonstrates the applicability of the findings through applications to ordinary differential equations. |
| format | Article |
| id | doaj-art-9c49bcd6d0ac4f46a0573f70ec22bab0 |
| institution | DOAJ |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-9c49bcd6d0ac4f46a0573f70ec22bab02025-08-20T02:44:44ZengMDPI AGAxioms2075-16802025-02-0114213510.3390/axioms14020135Certain Fixed-Point Results for (<inline-formula><math display="inline"><semantics><mrow><mi mathvariant="fraktur">e</mi></mrow></semantics></math></inline-formula>,<i>ψ</i>,Φ)-Enriched Weak Contractions via Theoretic Order with ApplicationsUmar Ishtiaq0Muhammad Din1Yumnam Rohen2Khalid A. Alnowibet3Ioan-Lucian Popa4Office of Research, Innovation and Commecialization, University of Management and Technology, Lahore 54770, PakistanDepartment of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Khlong Luang 12120, ThailandDepartment of Mathematics, Manipur University, Imphal 795003, IndiaStatistics and Operations Research Department, College of Science, King Saud University, Riyadh 11451, Saudi ArabiaDepartment of Computing, Mathematics and Electronics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, RomaniaThis paper aims to establish several fixed-point theorems within the framework of Banach spaces endowed with a binary relation. By utilizing enriched contraction principles involving two classes of altering-distance functions, the study encompasses various types of contractive mappings, including theoretic-order contractions, Picard–Banach contractions, weak contractions, and non-expansive contractions. A suitable Krasnoselskij iterative scheme is employed to derive the results. Many well-known fixed-point theorems (FPTs) can be obtained as special cases of these findings by assigning specific control functions in the main definitions or selecting an appropriate binary relation. To validate the theoretical results, numerous illustrative examples are provided. Furthermore, the paper demonstrates the applicability of the findings through applications to ordinary differential equations.https://www.mdpi.com/2075-1680/14/2/135theoretic-order contractionbinary relationsenriched contractionweak contractionsaltering-distance functions1st- and 2nd-order ordinary differential equations |
| spellingShingle | Umar Ishtiaq Muhammad Din Yumnam Rohen Khalid A. Alnowibet Ioan-Lucian Popa Certain Fixed-Point Results for (<inline-formula><math display="inline"><semantics><mrow><mi mathvariant="fraktur">e</mi></mrow></semantics></math></inline-formula>,<i>ψ</i>,Φ)-Enriched Weak Contractions via Theoretic Order with Applications Axioms theoretic-order contraction binary relations enriched contraction weak contractions altering-distance functions 1st- and 2nd-order ordinary differential equations |
| title | Certain Fixed-Point Results for (<inline-formula><math display="inline"><semantics><mrow><mi mathvariant="fraktur">e</mi></mrow></semantics></math></inline-formula>,<i>ψ</i>,Φ)-Enriched Weak Contractions via Theoretic Order with Applications |
| title_full | Certain Fixed-Point Results for (<inline-formula><math display="inline"><semantics><mrow><mi mathvariant="fraktur">e</mi></mrow></semantics></math></inline-formula>,<i>ψ</i>,Φ)-Enriched Weak Contractions via Theoretic Order with Applications |
| title_fullStr | Certain Fixed-Point Results for (<inline-formula><math display="inline"><semantics><mrow><mi mathvariant="fraktur">e</mi></mrow></semantics></math></inline-formula>,<i>ψ</i>,Φ)-Enriched Weak Contractions via Theoretic Order with Applications |
| title_full_unstemmed | Certain Fixed-Point Results for (<inline-formula><math display="inline"><semantics><mrow><mi mathvariant="fraktur">e</mi></mrow></semantics></math></inline-formula>,<i>ψ</i>,Φ)-Enriched Weak Contractions via Theoretic Order with Applications |
| title_short | Certain Fixed-Point Results for (<inline-formula><math display="inline"><semantics><mrow><mi mathvariant="fraktur">e</mi></mrow></semantics></math></inline-formula>,<i>ψ</i>,Φ)-Enriched Weak Contractions via Theoretic Order with Applications |
| title_sort | certain fixed point results for inline formula math display inline semantics mrow mi mathvariant fraktur e mi mrow semantics math inline formula i ψ i φ enriched weak contractions via theoretic order with applications |
| topic | theoretic-order contraction binary relations enriched contraction weak contractions altering-distance functions 1st- and 2nd-order ordinary differential equations |
| url | https://www.mdpi.com/2075-1680/14/2/135 |
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