Abstraction of Interpolative Reich-Rus-Ćirić-Type Contractions and Simplest Proof Technique
The concept of symmetry is a very vast topic that is involved in the studies of several phenomena. This concept enables us to discuss the phenomenon in some systematic pattern depending upon the type of phenomenon. Each phenomenon has its own type of symmetry. The phenomenon that is used in the disc...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-07-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/8/1504 |
| _version_ | 1797407774334779392 |
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| author | Monairah Alansari Muhammad Usman Ali |
| author_facet | Monairah Alansari Muhammad Usman Ali |
| author_sort | Monairah Alansari |
| collection | DOAJ |
| description | The concept of symmetry is a very vast topic that is involved in the studies of several phenomena. This concept enables us to discuss the phenomenon in some systematic pattern depending upon the type of phenomenon. Each phenomenon has its own type of symmetry. The phenomenon that is used in the discussion of this article is a symmetric distance-measuring function. This article presents the notions of abstract interpolative Reich-Rus-Ćirić-type contractions with a shrink map and examines the existence of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula>-fixed points for such maps in complete metric space. These notions are defined through special types of simulation functions. The proof technique of the results presented in this article is easy to understand compared with the existing literature on interpolative Reich-Rus-Ćirić-type contractions. |
| first_indexed | 2024-03-09T03:47:26Z |
| format | Article |
| id | doaj.art-79c23439d306411b92d9c3761809d058 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T03:47:26Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-79c23439d306411b92d9c3761809d0582023-12-03T14:32:30ZengMDPI AGSymmetry2073-89942022-07-01148150410.3390/sym14081504Abstraction of Interpolative Reich-Rus-Ćirić-Type Contractions and Simplest Proof TechniqueMonairah Alansari0Muhammad Usman Ali1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, COMSATS University Islamabad, Attock Campus, Attock 43600, PakistanThe concept of symmetry is a very vast topic that is involved in the studies of several phenomena. This concept enables us to discuss the phenomenon in some systematic pattern depending upon the type of phenomenon. Each phenomenon has its own type of symmetry. The phenomenon that is used in the discussion of this article is a symmetric distance-measuring function. This article presents the notions of abstract interpolative Reich-Rus-Ćirić-type contractions with a shrink map and examines the existence of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula>-fixed points for such maps in complete metric space. These notions are defined through special types of simulation functions. The proof technique of the results presented in this article is easy to understand compared with the existing literature on interpolative Reich-Rus-Ćirić-type contractions.https://www.mdpi.com/2073-8994/14/8/1504<i>ϕ</i>-fixed pointsinterpolative Kannan contractionabstract interpolative Reich-Rus-Ćirić-type contractions with a shrink map |
| spellingShingle | Monairah Alansari Muhammad Usman Ali Abstraction of Interpolative Reich-Rus-Ćirić-Type Contractions and Simplest Proof Technique Symmetry <i>ϕ</i>-fixed points interpolative Kannan contraction abstract interpolative Reich-Rus-Ćirić-type contractions with a shrink map |
| title | Abstraction of Interpolative Reich-Rus-Ćirić-Type Contractions and Simplest Proof Technique |
| title_full | Abstraction of Interpolative Reich-Rus-Ćirić-Type Contractions and Simplest Proof Technique |
| title_fullStr | Abstraction of Interpolative Reich-Rus-Ćirić-Type Contractions and Simplest Proof Technique |
| title_full_unstemmed | Abstraction of Interpolative Reich-Rus-Ćirić-Type Contractions and Simplest Proof Technique |
| title_short | Abstraction of Interpolative Reich-Rus-Ćirić-Type Contractions and Simplest Proof Technique |
| title_sort | abstraction of interpolative reich rus ciric type contractions and simplest proof technique |
| topic | <i>ϕ</i>-fixed points interpolative Kannan contraction abstract interpolative Reich-Rus-Ćirić-type contractions with a shrink map |
| url | https://www.mdpi.com/2073-8994/14/8/1504 |
| work_keys_str_mv | AT monairahalansari abstractionofinterpolativereichruscirictypecontractionsandsimplestprooftechnique AT muhammadusmanali abstractionofinterpolativereichruscirictypecontractionsandsimplestprooftechnique |