Remarks on “Perov Fixed-Point Results on F-Contraction Mappings Equipped with Binary Relation”
Since 1964, when I.A. Perov introduced the so-called generalized metric space where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mo>(</mo><mi>x</mi><mo&...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/6/518 |
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| author | Slobodanka Mitrović Nicola Fabiano Slobodan Radojević Stojan Radenović |
| author_facet | Slobodanka Mitrović Nicola Fabiano Slobodan Radojević Stojan Radenović |
| author_sort | Slobodanka Mitrović |
| collection | DOAJ |
| description | Since 1964, when I.A. Perov introduced the so-called generalized metric space where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow></semantics></math></inline-formula> is an element of the vector space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mi>m</mi></msup></semantics></math></inline-formula>, many researchers have considered various contractive conditions in this type of space. In this paper, we generalize, extend and unify some of those established results. We are primarily concerned with examining the existence of a fixed point of some mapping from <i>X</i> to itself, but if <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow></semantics></math></inline-formula> belongs to some relation <i>R</i> on the set <i>X</i>, then the binary relation <i>R</i> and some F contraction defined on the space cone <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mi>m</mi></msup></semantics></math></inline-formula> are combined. We start our consideration with the recently announced results and give them strict, critical remarks. In addition, we improve several announced results by weakening some of the given conditions. |
| first_indexed | 2024-03-11T02:46:36Z |
| format | Article |
| id | doaj.art-373ef3dc15b441c4bffc4968790b4cad |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T02:46:36Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-373ef3dc15b441c4bffc4968790b4cad2023-11-18T09:16:11ZengMDPI AGAxioms2075-16802023-05-0112651810.3390/axioms12060518Remarks on “Perov Fixed-Point Results on F-Contraction Mappings Equipped with Binary Relation”Slobodanka Mitrović0Nicola Fabiano1Slobodan Radojević2Stojan Radenović3Faculty of Forestry, Kneza Višeslava 1, University of Belgrade, 11030 Beograd, SerbiaVinča Institute of Nuclear Sciences-National Institute of the Republic of Serbia, University of Belgrade, Mike Petrovića Alasa 12-14, 11351 Beograd, SerbiaFaculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd, SerbiaFaculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd, SerbiaSince 1964, when I.A. Perov introduced the so-called generalized metric space where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow></semantics></math></inline-formula> is an element of the vector space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mi>m</mi></msup></semantics></math></inline-formula>, many researchers have considered various contractive conditions in this type of space. In this paper, we generalize, extend and unify some of those established results. We are primarily concerned with examining the existence of a fixed point of some mapping from <i>X</i> to itself, but if <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow></semantics></math></inline-formula> belongs to some relation <i>R</i> on the set <i>X</i>, then the binary relation <i>R</i> and some F contraction defined on the space cone <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mi>m</mi></msup></semantics></math></inline-formula> are combined. We start our consideration with the recently announced results and give them strict, critical remarks. In addition, we improve several announced results by weakening some of the given conditions.https://www.mdpi.com/2075-1680/12/6/518binary relationvector-valued metric spacefixed pointF contractionPerov’s type mapping |
| spellingShingle | Slobodanka Mitrović Nicola Fabiano Slobodan Radojević Stojan Radenović Remarks on “Perov Fixed-Point Results on F-Contraction Mappings Equipped with Binary Relation” Axioms binary relation vector-valued metric space fixed point F contraction Perov’s type mapping |
| title | Remarks on “Perov Fixed-Point Results on F-Contraction Mappings Equipped with Binary Relation” |
| title_full | Remarks on “Perov Fixed-Point Results on F-Contraction Mappings Equipped with Binary Relation” |
| title_fullStr | Remarks on “Perov Fixed-Point Results on F-Contraction Mappings Equipped with Binary Relation” |
| title_full_unstemmed | Remarks on “Perov Fixed-Point Results on F-Contraction Mappings Equipped with Binary Relation” |
| title_short | Remarks on “Perov Fixed-Point Results on F-Contraction Mappings Equipped with Binary Relation” |
| title_sort | remarks on perov fixed point results on f contraction mappings equipped with binary relation |
| topic | binary relation vector-valued metric space fixed point F contraction Perov’s type mapping |
| url | https://www.mdpi.com/2075-1680/12/6/518 |
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