{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:10:38Z","timestamp":1760148638381,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,5,25]],"date-time":"2023-05-25T00:00:00Z","timestamp":1684972800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Since 1964, when I.A. Perov introduced the so-called generalized metric space where d(x,y) is an element of the vector space Rm, 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 X to itself, but if (x,y) belongs to some relation R on the set X, then the binary relation R and some F contraction defined on the space cone Rm 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.<\/jats:p>","DOI":"10.3390\/axioms12060518","type":"journal-article","created":{"date-parts":[[2023,5,26]],"date-time":"2023-05-26T02:05:44Z","timestamp":1685066744000},"page":"518","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Remarks on \u201cPerov Fixed-Point Results on F-Contraction Mappings Equipped with Binary Relation\u201d"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5915-2234","authenticated-orcid":false,"given":"Slobodanka","family":"Mitrovi\u0107","sequence":"first","affiliation":[{"name":"Faculty of Forestry, Kneza Vi\u0161eslava 1, University of Belgrade, 11030 Beograd, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1645-2071","authenticated-orcid":false,"given":"Nicola","family":"Fabiano","sequence":"additional","affiliation":[{"name":"Vin\u010da Institute of Nuclear Sciences-National Institute of the Republic of Serbia, University of Belgrade, Mike Petrovi\u0107a Alasa 12-14, 11351 Beograd, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1845-4441","authenticated-orcid":false,"given":"Slobodan","family":"Radojevi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8254-6688","authenticated-orcid":false,"given":"Stojan","family":"Radenovi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"133","DOI":"10.4064\/fm-3-1-133-181","article-title":"Sur les op\u00e9rations dans les ensembles abstraits et leur application aux \u00e9quations int\u00e9grales","volume":"3","author":"Banach","year":"1922","journal-title":"Fundam. Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1016\/j.jmaa.2007.09.070","article-title":"Common fixed point results for noncommuting mappings without continuity in cone metric space","volume":"341","author":"Abbas","year":"2008","journal-title":"J. Math. Anal. Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1007\/s11784-015-0247-y","article-title":"Relation-theoretic contraction principle","volume":"17","author":"Alam","year":"2015","journal-title":"J. Fixed Point Theory Appl."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"20199","DOI":"10.3934\/math.20221105","article-title":"Perov-fixed point theorems on a metric space equipped with ordered theoretic relation","volume":"7","author":"Almalki","year":"2022","journal-title":"Aims Math."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1007\/s11784-020-00779-4","article-title":"Fixed point results for Perov type F-contractions and an application","volume":"22","author":"Altun","year":"2020","journal-title":"J. Fixed Point Theory Appl."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Din, F.U., Din, M., Ishtiaq, U., and Sessa, S. (2023). Perov fixed-point results on F-contraction mappings equipped with binary relation. Mathematics, 11.","DOI":"10.3390\/math11010238"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Rhoades, B.E. (1977). A Comparison of Various Definitions of Contractive Mappings, Transactions of the American Mathematical Society.","DOI":"10.1090\/S0002-9947-1977-0433430-4"},{"key":"ref_8","first-page":"141","article-title":"Solving fractional differential equations using fixed point results in generalized metric spaces of Perov\u2019s type","volume":"14","author":"Fabiano","year":"2023","journal-title":"Press. Twms. App. Eng. Math."},{"key":"ref_9","first-page":"367","article-title":"Around Perov\u2019s fixed point theorem for mappings on generalized metric spaces","volume":"17","author":"Jachymski","year":"2016","journal-title":"Fixed Point Theory"},{"key":"ref_10","first-page":"1563","article-title":"Tableaux ramifies densambles","volume":"198","author":"Kurepa","year":"1934","journal-title":"C. R. Acad. Sci. Paris"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Mirkov, N., Radenovi\u0107, S., and Radojevi\u0107, S. (2021). Some New Observations for F-Contractions in Vector-Valued Metric Spaces of Perov\u2019s Type. Axioms, 10.","DOI":"10.3390\/axioms10020127"},{"key":"ref_12","first-page":"90","article-title":"Critical remarks on \u201cA new fixed point result of Perov type and its application to a semilinear operator system\u201d","volume":"14","author":"Mirkov","year":"2023","journal-title":"TWMS J. Pure Appl. Math."},{"key":"ref_13","first-page":"115","article-title":"On Cauchy problem for a system of ordinary differential equations","volume":"2","author":"Perov","year":"1964","journal-title":"Priblizhen. Met. Reshen. Diff. Uravn."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"187","DOI":"10.3934\/math.2022011","article-title":"Some significant remarks on multivalued Perov type contractions on cone metric spaces with a directed graph","volume":"7","author":"Fabiano","year":"2021","journal-title":"Aims Math."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1186\/1687-1812-2012-94","article-title":"Fixed points of a new type of contractive mappings in complete metric spaces","volume":"2012","author":"Wardowski","year":"2012","journal-title":"Fixed Point Theory Appl."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"327","DOI":"10.37256\/cm.3320221517","article-title":"On F-contractions: A Survey","volume":"3","author":"Fabiano","year":"2022","journal-title":"Contemp. Math."},{"key":"ref_17","first-page":"93","article-title":"Generalized -contractions in Partially Ordered Metric Spaces","volume":"16","author":"Razavi","year":"2019","journal-title":"Sahand Commun. Math. Anal."},{"key":"ref_18","first-page":"146","article-title":"Fixed points of F-weak contractions on complete metric spaces","volume":"47","author":"Wardowski","year":"2014","journal-title":"Demonstr. Math."},{"key":"ref_19","first-page":"147","article-title":"Iterative approximation of fixed points for Pre\u0161i\u0107 type F-contraction operators","volume":"78","author":"Abbas","year":"2016","journal-title":"UPB Sci. Bull. Ser. A"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1186\/s13663-015-0333-2","article-title":"New fixed point theorems for generalized F-contractions in complete metric spaces","volume":"2015","author":"Ahmad","year":"2015","journal-title":"Fixed Point Theory Appl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"63","DOI":"10.18576\/jant\/050110","article-title":"Two new fixed point results for generalized Wardowski type contractions","volume":"5","author":"Ameer","year":"2017","journal-title":"J. Anal. Num. Theory"},{"key":"ref_22","first-page":"129","article-title":"Hardy-Rogers-type fixed point theorems for \u03b1-GF-contractions","volume":"51","author":"Arshad","year":"2015","journal-title":"Arch. Math."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"79","DOI":"10.17654\/FP011010079","article-title":"Fixed point results for F-contractions involving some new rational expressions","volume":"11","author":"Arshad","year":"2016","journal-title":"J. Fixed Point Theory Appl."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"743","DOI":"10.1007\/s10013-015-0123-5","article-title":"A fixed point theorem for generalized F-contractions on complete metric spaces","volume":"43","author":"Dung","year":"2015","journal-title":"Vietnam J. Math."},{"key":"ref_25","first-page":"57","article-title":"A new generalization of Wardowski fixed point theorem in complete metric spaces","volume":"1","author":"Fulga","year":"2017","journal-title":"Adv. Theory Nonlinear Anal. Appl."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"8728","DOI":"10.3934\/math.2021507","article-title":"Fixed point results of a generalized reversed F-contraction mapping and its application","volume":"6","author":"Bashir","year":"2021","journal-title":"AIMS Math."},{"key":"ref_27","first-page":"jnaa-00211","article-title":"Fixed point theorem for F\u03c9-contractions in complete metric spaces","volume":"2013","author":"Batra","year":"2013","journal-title":"J. Nonlin. Anal. Appl."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1315","DOI":"10.12988\/ijma.2014.45147","article-title":"Coincidence point theorem for a new type of contractive on metric spaces","volume":"8","author":"Batra","year":"2014","journal-title":"Int. J. Math. Anal."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"715","DOI":"10.2298\/FIL1404715C","article-title":"Fixed point results for F-contractive mappings of Hardy-Rogers-type","volume":"28","author":"Cosentino","year":"2014","journal-title":"Filomat"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1585","DOI":"10.1090\/proc\/13808","article-title":"Solving existence problems via F-contractions","volume":"146","author":"Wardowski","year":"2018","journal-title":"Proc. Amer. Math. 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