Fixed Point Theorems for Nonexpansive Mappings under Binary Relations
In the present article, we establish relation-theoretic fixed point theorems in a Banach space, satisfying the Opial condition, using the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script...
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| Format: | Article |
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MDPI AG
2021-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/17/2059 |
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| author | Aftab Alam Reny George Mohammad Imdad Md Hasanuzzaman |
| author_facet | Aftab Alam Reny George Mohammad Imdad Md Hasanuzzaman |
| author_sort | Aftab Alam |
| collection | DOAJ |
| description | In the present article, we establish relation-theoretic fixed point theorems in a Banach space, satisfying the Opial condition, using the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">R</mi></semantics></math></inline-formula>-Krasnoselskii sequence. We observe that graphical versions (Fixed Point Theory Appl. 2015:49 (2015) 6 pp.) and order-theoretic versions (Fixed Point Theory Appl. 2015:110 (2015) 7 pp.) of such results can be extended to a transitive binary relation. |
| first_indexed | 2024-03-10T08:08:19Z |
| format | Article |
| id | doaj.art-e97a7dba664746a09d988801ae53e059 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T08:08:19Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-e97a7dba664746a09d988801ae53e0592023-11-22T10:57:18ZengMDPI AGMathematics2227-73902021-08-01917205910.3390/math9172059Fixed Point Theorems for Nonexpansive Mappings under Binary RelationsAftab Alam0Reny George1Mohammad Imdad2Md Hasanuzzaman3Department of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaDepartment of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi ArabiaDepartment of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaDepartment of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaIn the present article, we establish relation-theoretic fixed point theorems in a Banach space, satisfying the Opial condition, using the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">R</mi></semantics></math></inline-formula>-Krasnoselskii sequence. We observe that graphical versions (Fixed Point Theory Appl. 2015:49 (2015) 6 pp.) and order-theoretic versions (Fixed Point Theory Appl. 2015:110 (2015) 7 pp.) of such results can be extended to a transitive binary relation.https://www.mdpi.com/2227-7390/9/17/2059binary relationℛ-nonexpansive mapsuniformly convex Banach spaceℛ-Krasnoselskii sequence |
| spellingShingle | Aftab Alam Reny George Mohammad Imdad Md Hasanuzzaman Fixed Point Theorems for Nonexpansive Mappings under Binary Relations Mathematics binary relation ℛ-nonexpansive maps uniformly convex Banach space ℛ-Krasnoselskii sequence |
| title | Fixed Point Theorems for Nonexpansive Mappings under Binary Relations |
| title_full | Fixed Point Theorems for Nonexpansive Mappings under Binary Relations |
| title_fullStr | Fixed Point Theorems for Nonexpansive Mappings under Binary Relations |
| title_full_unstemmed | Fixed Point Theorems for Nonexpansive Mappings under Binary Relations |
| title_short | Fixed Point Theorems for Nonexpansive Mappings under Binary Relations |
| title_sort | fixed point theorems for nonexpansive mappings under binary relations |
| topic | binary relation ℛ-nonexpansive maps uniformly convex Banach space ℛ-Krasnoselskii sequence |
| url | https://www.mdpi.com/2227-7390/9/17/2059 |
| work_keys_str_mv | AT aftabalam fixedpointtheoremsfornonexpansivemappingsunderbinaryrelations AT renygeorge fixedpointtheoremsfornonexpansivemappingsunderbinaryrelations AT mohammadimdad fixedpointtheoremsfornonexpansivemappingsunderbinaryrelations AT mdhasanuzzaman fixedpointtheoremsfornonexpansivemappingsunderbinaryrelations |