Refinements to Relation-Theoretic Contraction Principle
After the appearance of relation-theoretic contraction principle proved in a metric space equipped with an amorphous binary relation (often termed as relational metric space), various core fixed point results have been proved in the setting of different relational distance spaces by varying underlyi...
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MDPI AG
2022-06-01
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| Online Access: | https://www.mdpi.com/2075-1680/11/7/316 |
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| author | Aftab Alam Reny George Mohammad Imdad |
| author_facet | Aftab Alam Reny George Mohammad Imdad |
| author_sort | Aftab Alam |
| collection | DOAJ |
| description | After the appearance of relation-theoretic contraction principle proved in a metric space equipped with an amorphous binary relation (often termed as relational metric space), various core fixed point results have been proved in the setting of different relational distance spaces by varying underlying contraction conditions. In proving such results, the notions of completeness of ambient space, continuity of involved mapping and <i>d</i>-self-closedness of underlying binary relation are of paramount importance. The aim of this paper is to further refine the relation-theoretic contraction principle by relaxing the conditions of completeness and continuity by replacing their respective relation-theoretic analogues. Moreover, we observe that the notion of <i>d</i>-self-closedness utilized in relation-theoretic contraction principle is more general than the concepts of regularity and strong regularity utilized by earlier authors. |
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| format | Article |
| id | doaj.art-c2b16887f049491e91b402fa8a08adb6 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T10:23:29Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-c2b16887f049491e91b402fa8a08adb62023-12-01T21:53:21ZengMDPI AGAxioms2075-16802022-06-0111731610.3390/axioms11070316Refinements to Relation-Theoretic Contraction PrincipleAftab Alam0Reny George1Mohammad Imdad2Department of Mathematics, Jamia Millia Islamia, New Delhi 110025, IndiaDepartment of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Alkharj 11942, Saudi ArabiaDepartment of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaAfter the appearance of relation-theoretic contraction principle proved in a metric space equipped with an amorphous binary relation (often termed as relational metric space), various core fixed point results have been proved in the setting of different relational distance spaces by varying underlying contraction conditions. In proving such results, the notions of completeness of ambient space, continuity of involved mapping and <i>d</i>-self-closedness of underlying binary relation are of paramount importance. The aim of this paper is to further refine the relation-theoretic contraction principle by relaxing the conditions of completeness and continuity by replacing their respective relation-theoretic analogues. Moreover, we observe that the notion of <i>d</i>-self-closedness utilized in relation-theoretic contraction principle is more general than the concepts of regularity and strong regularity utilized by earlier authors.https://www.mdpi.com/2075-1680/11/7/316<named-content content-type="equation"><inline-formula> <mml:math id="mm200"> <mml:semantics> <mml:mi mathvariant="script">R</mml:mi> </mml:semantics> </mml:math> </inline-formula></named-content>-continuous mappings<i>T</i>-closed binary relations<named-content content-type="equation"><inline-formula> <mml:math id="mm201"> <mml:semantics> <mml:mi mathvariant="script">R</mml:mi> </mml:semantics> </mml:math> </inline-formula></named-content>-connected sets |
| spellingShingle | Aftab Alam Reny George Mohammad Imdad Refinements to Relation-Theoretic Contraction Principle Axioms <named-content content-type="equation"><inline-formula> <mml:math id="mm200"> <mml:semantics> <mml:mi mathvariant="script">R</mml:mi> </mml:semantics> </mml:math> </inline-formula></named-content>-continuous mappings <i>T</i>-closed binary relations <named-content content-type="equation"><inline-formula> <mml:math id="mm201"> <mml:semantics> <mml:mi mathvariant="script">R</mml:mi> </mml:semantics> </mml:math> </inline-formula></named-content>-connected sets |
| title | Refinements to Relation-Theoretic Contraction Principle |
| title_full | Refinements to Relation-Theoretic Contraction Principle |
| title_fullStr | Refinements to Relation-Theoretic Contraction Principle |
| title_full_unstemmed | Refinements to Relation-Theoretic Contraction Principle |
| title_short | Refinements to Relation-Theoretic Contraction Principle |
| title_sort | refinements to relation theoretic contraction principle |
| topic | <named-content content-type="equation"><inline-formula> <mml:math id="mm200"> <mml:semantics> <mml:mi mathvariant="script">R</mml:mi> </mml:semantics> </mml:math> </inline-formula></named-content>-continuous mappings <i>T</i>-closed binary relations <named-content content-type="equation"><inline-formula> <mml:math id="mm201"> <mml:semantics> <mml:mi mathvariant="script">R</mml:mi> </mml:semantics> </mml:math> </inline-formula></named-content>-connected sets |
| url | https://www.mdpi.com/2075-1680/11/7/316 |
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