Recent Advancements in KRH-Interpolative-Type Contractions
The focus of this paper is to conduct a comprehensive analysis of the advancements made in the understanding of Interpolative contraction, building upon the ideas initially introduced by Karapinar in 2018. In this paper, we develop the notion of Interpolative contraction mappings to the case of non-...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-08-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/15/8/1515 |
| _version_ | 1797583226320977920 |
|---|---|
| author | Ansar Abbas Amjad Ali Hamed Al Sulami Aftab Hussain |
| author_facet | Ansar Abbas Amjad Ali Hamed Al Sulami Aftab Hussain |
| author_sort | Ansar Abbas |
| collection | DOAJ |
| description | The focus of this paper is to conduct a comprehensive analysis of the advancements made in the understanding of Interpolative contraction, building upon the ideas initially introduced by Karapinar in 2018. In this paper, we develop the notion of Interpolative contraction mappings to the case of non-linear Kannan Interpolative, Riech Rus Ćirić interpolative and Hardy–Roger Interpolative contraction mappings based on controlled function, and prove some fixed point results in the context of controlled metric space, thereby enhancing the current understanding of this particular analysis. Furthermore, we provide a concrete example that illustrates the underlying drive for the investigations presented in this context. An application of the proposed non-linear Interpolative-contractions to the Liouville–Caputo fractional derivatives and fractional differential equations is provided in this paper. |
| first_indexed | 2024-03-10T23:32:51Z |
| format | Article |
| id | doaj.art-a831ac61577d44b29c7c60b617f8dd4b |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T23:32:51Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-a831ac61577d44b29c7c60b617f8dd4b2023-11-19T03:10:51ZengMDPI AGSymmetry2073-89942023-08-01158151510.3390/sym15081515Recent Advancements in KRH-Interpolative-Type ContractionsAnsar Abbas0Amjad Ali1Hamed Al Sulami2Aftab Hussain3Department of Mathematics & Statistics, International Islamic University, Islamabad 44000, PakistanDepartment of Mathematics & Statistics, International Islamic University, Islamabad 44000, PakistanDepartment of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaThe focus of this paper is to conduct a comprehensive analysis of the advancements made in the understanding of Interpolative contraction, building upon the ideas initially introduced by Karapinar in 2018. In this paper, we develop the notion of Interpolative contraction mappings to the case of non-linear Kannan Interpolative, Riech Rus Ćirić interpolative and Hardy–Roger Interpolative contraction mappings based on controlled function, and prove some fixed point results in the context of controlled metric space, thereby enhancing the current understanding of this particular analysis. Furthermore, we provide a concrete example that illustrates the underlying drive for the investigations presented in this context. An application of the proposed non-linear Interpolative-contractions to the Liouville–Caputo fractional derivatives and fractional differential equations is provided in this paper.https://www.mdpi.com/2073-8994/15/8/1515fixed pointKRH-Interpolative contraction mappingscontrolled metric spaceLiouville–Caputo fractional derivativesfractional differential equations |
| spellingShingle | Ansar Abbas Amjad Ali Hamed Al Sulami Aftab Hussain Recent Advancements in KRH-Interpolative-Type Contractions Symmetry fixed point KRH-Interpolative contraction mappings controlled metric space Liouville–Caputo fractional derivatives fractional differential equations |
| title | Recent Advancements in KRH-Interpolative-Type Contractions |
| title_full | Recent Advancements in KRH-Interpolative-Type Contractions |
| title_fullStr | Recent Advancements in KRH-Interpolative-Type Contractions |
| title_full_unstemmed | Recent Advancements in KRH-Interpolative-Type Contractions |
| title_short | Recent Advancements in KRH-Interpolative-Type Contractions |
| title_sort | recent advancements in krh interpolative type contractions |
| topic | fixed point KRH-Interpolative contraction mappings controlled metric space Liouville–Caputo fractional derivatives fractional differential equations |
| url | https://www.mdpi.com/2073-8994/15/8/1515 |
| work_keys_str_mv | AT ansarabbas recentadvancementsinkrhinterpolativetypecontractions AT amjadali recentadvancementsinkrhinterpolativetypecontractions AT hamedalsulami recentadvancementsinkrhinterpolativetypecontractions AT aftabhussain recentadvancementsinkrhinterpolativetypecontractions |