{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:51:04Z","timestamp":1760147464881,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,6]],"date-time":"2023-02-06T00:00:00Z","timestamp":1675641600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>After the appearance of relation-theoretic contraction principle due to Alam and Imdad, the domain of fixed point theory applied to relational metric spaces has attracted much attention. Existence and uniqueness of fixed\/coincidence points satisfying the different types of contractivity conditions in the framework of relational metric space have been studied in recent times. Such results have the great advantage to solve certain types of matrix equations and boundary value problems for ordinary differential equations, integral equations and fractional differential equations. This article is devoted to proving the coincidence and common fixed point theorems for a pair of mappings (T,S) employing relation-theoretic (\u03d5,\u03c8)-contractions in a metric space equipped with a locally finitely T-transitive relation. Our results improve, modify, enrich and unify several existing coincidence points as well as fixed point results. Several examples are provided to substantiate the utility of our results.<\/jats:p>","DOI":"10.3390\/sym15020434","type":"journal-article","created":{"date-parts":[[2023,2,6]],"date-time":"2023-02-06T04:59:10Z","timestamp":1675659550000},"page":"434","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Coincidence Theorems under Generalized Nonlinear Relational Contractions"],"prefix":"10.3390","volume":"15","author":[{"given":"Nifeen Hussain","family":"Altaweel","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia"}]},{"given":"Nidal H. E.","family":"Eljaneid","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia"}]},{"given":"Hamid I. A.","family":"Mohammed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia"}]},{"given":"Ibtisam M.","family":"Alanazi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8734-5516","authenticated-orcid":false,"given":"Faizan Ahmad","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,6]]},"reference":[{"key":"ref_1","first-page":"733","article-title":"A coincidence theorem","volume":"16","author":"Goebel","year":"1968","journal-title":"Bull. Acad. Pol. Sci. S\u00e9r. Sci. Math. Astron. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1080\/00029890.1976.11994093","article-title":"Commuting maps and fixed points","volume":"83","author":"Jungck","year":"1976","journal-title":"Am. Math. Mon."},{"key":"ref_3","first-page":"199","article-title":"Common fixed points for noncontinuous nonself maps on non-metric spaces","volume":"4","author":"Jungck","year":"1996","journal-title":"Far East J. Math. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"771","DOI":"10.1155\/S0161171286000935","article-title":"Compatible mappings and common fixed points","volume":"9","author":"Jungck","year":"1986","journal-title":"Int. J. Math. Math. Sci."},{"key":"ref_5","first-page":"149","article-title":"On a weak commutativity condition of mappings in fixed point considerations","volume":"32","author":"Sessa","year":"1982","journal-title":"Publ. Inst. Math. Soc."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1006\/jmaa.1999.6559","article-title":"Common fixed points of Lipschitz type mapping pairs","volume":"240","author":"Pant","year":"1999","journal-title":"J. Math. Anal. Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"731","DOI":"10.1006\/jmaa.2000.7082","article-title":"Common fixed points of two partially commuting tangential selfmaps on a metric space","volume":"250","author":"Sastry","year":"2000","journal-title":"J. Math. Anal. Appl."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/S0022-247X(02)00059-8","article-title":"Some new common fixed point theorems under strict contractive conditions","volume":"270","author":"Aamri","year":"2002","journal-title":"J. Math. Anal. Appl."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"697151","DOI":"10.1155\/2013\/697151","article-title":"A note on various classes of compatible-type pairs of mappings and common fixed point theorems","volume":"2013","author":"Kadelburg","year":"2013","journal-title":"Abstr. Appl. Anal."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1186\/1687-1812-2014-38","article-title":"Comparison of various noncommuting conditions in metric fixed point theory and their applications","volume":"2014","author":"Agarwal","year":"2014","journal-title":"Fixed Point Theory Appl."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1186\/1687-1812-2014-216","article-title":"Some coincidence theorems for generalized nonlinear contractions in ordered metric spaces with applications","volume":"2014","author":"Alam","year":"2014","journal-title":"Fixed Point Theory Appl."},{"key":"ref_12","first-page":"1059","article-title":"Remarks on certain noted coincidence theorems: A unifying and enriching approach","volume":"26","author":"Alam","year":"2021","journal-title":"Nonlinear Funct. Anal. Appl."},{"key":"ref_13","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_14","doi-asserted-by":"crossref","first-page":"4421","DOI":"10.2298\/FIL1714421A","article-title":"Relation-theoretic metrical coincidence theorems","volume":"31","author":"Alam","year":"2017","journal-title":"Filomat"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1711","DOI":"10.1007\/s11784-016-0306-z","article-title":"Fixed point theorems for FR-contractions with applications to solution of nonlinear matrix equations","volume":"19","author":"Sawangsup","year":"2017","journal-title":"J. Fixed Point Theory Appl."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"13","DOI":"10.24193\/fpt-ro.2018.1.02","article-title":"Nonlinear contractions in metric spaces under locally T-transitive binary relations","volume":"19","author":"Alam","year":"2018","journal-title":"Fixed Point Theory"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"5829","DOI":"10.1007\/s40314-018-0664-9","article-title":"On solving nonlinear matrix equations in terms of b-simulation functions in b-metric spaces with numerical solutions","volume":"37","author":"Sawangsup","year":"2018","journal-title":"Comp. Appl. Math."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Al-Sulami, H.H., Ahmad, J., Hussain, N., and Latif, A. (2018). Relation-theoretic (\u03b8,R)-contraction results with applications to nonlinear matrix equations. Symmetry, 10.","DOI":"10.3390\/sym10120767"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"59","DOI":"10.18514\/MMN.2019.2468","article-title":"Metrical fixed point theorems via locally finitely T-transitive binary relations under certain control functions","volume":"20","author":"Alam","year":"2019","journal-title":"Miskolc Math. Notes"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1186\/s13663-019-0656-5","article-title":"Observations on relation-theoretic coincidence theorems under Boyd\u2013Wong type nonlinear contractions","volume":"2019","author":"Alam","year":"2019","journal-title":"Fixed Point Theory Appl."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Ameer, E., Nazam, M., Aydi, H., Arshad, M., and Mlaiki, N. (2019). On (\u039b,\u03a5,R)-contractions and applications to nonlinear matrix equations. Mathematics, 7.","DOI":"10.3390\/math7050443"},{"key":"ref_22","first-page":"89","article-title":"A relation theoretic approach for \u03d5-fixed point result in metric space with an application to an integral equation","volume":"6","author":"Gopal","year":"2019","journal-title":"Commun. Nonlinear Anal."},{"key":"ref_23","first-page":"6574695","article-title":"Employing locally finitely T-transitive binary relations to prove coincidence theorems for nonlinear contractions","volume":"2020","author":"Arif","year":"2020","journal-title":"J. Funct. Spaces"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Hossain, A., Khan, F.A., and Khan, Q.H. (2021). A relation-theoretic metrical fixed point theorem for rational type contraction mapping with an application. Axioms, 10.","DOI":"10.3390\/axioms10040316"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"171","DOI":"10.4067\/S0719-06462021000100171","article-title":"Existence, well-posedness of coupled fixed points and application to nonlinear integral equations","volume":"23","author":"Choudhury","year":"2021","journal-title":"Cubo"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Altaweel, N.H., and Khan, F.A. (2022). Relation-theoretic fixed point theorems involving certain auxiliary functions with applications. Symmetry, 14.","DOI":"10.3390\/sym14122614"},{"key":"ref_27","first-page":"3550923","article-title":"Relational Meir-Keeler contractions and common fixed point theorems","volume":"2022","author":"Khan","year":"2022","journal-title":"J. Funct. Spaces"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Alam, A., George, R., and Imdad, M. (2022). Refinements to relation-theoretic contraction principle. Axioms, 11.","DOI":"10.3390\/axioms11070316"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"4477660","DOI":"10.1155\/2022\/4477660","article-title":"Relational quasi-contractions and related fixed point theorems","volume":"2022","author":"Eljaneid","year":"2022","journal-title":"J. Math."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"71","DOI":"10.18514\/MMN.2022.3220","article-title":"Fixed point theorems under locally T-transitive binary relations employing Matkowski contractions","volume":"23","author":"Arif","year":"2022","journal-title":"Miskolc Math. Notes"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Khan, F.A. (2022). Almost contractions under binary relations. Axioms, 11.","DOI":"10.3390\/axioms11090441"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Khan, F.A. (2022). (\u03c8,\u03d5)-contractions under a class of transitive binary relations. Symmetry, 14.","DOI":"10.3390\/sym14102111"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"406368","DOI":"10.1155\/2008\/406368","article-title":"A generalization of contraction principle in metric spaces","volume":"2008","author":"Dutta","year":"2008","journal-title":"Fixed Point Theory Appl."},{"key":"ref_34","first-page":"23","article-title":"Discussion on generalized nonlinear contractions","volume":"84","author":"Alam","year":"2022","journal-title":"Politehn. Univ. Buchar. Sci. Bull. Ser. A Appl. Math. Phys."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"6634","DOI":"10.3934\/math.2022370","article-title":"Relation-preserving generalized nonlinear contractions and related fixed point theorems","volume":"7","author":"Sk","year":"2022","journal-title":"AIMS Math."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1188","DOI":"10.1016\/j.na.2009.08.003","article-title":"Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations","volume":"72","author":"Harjani","year":"2010","journal-title":"Nonlinear Anal."},{"key":"ref_37","unstructured":"Lipschutz, S. (1964). Schaum\u2019s Outlines of Theory and Problems of Set Theory and Related Topics, McGraw-Hill."},{"key":"ref_38","unstructured":"Kolman, B., Busby, R.C., and Ross, S. (2000). Discrete Mathematical Structures, PHI. [3rd ed.]."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1186\/1687-1812-2013-205","article-title":"Fixed Point results for (\u03b1\u03c8,\u03b2\u03d5)-contractive mappings for a generalized altering distance","volume":"2013","author":"Berzig","year":"2013","journal-title":"Fixed Point Theory Appl."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"169358","DOI":"10.1155\/2014\/169358","article-title":"Contractive maps in locally transitive relational metric spaces","volume":"2014","author":"Turinici","year":"2014","journal-title":"The Sci. World J."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1007\/978-1-4939-1246-9_18","article-title":"Contractive operators in relational metric spaces","volume":"Volume 95","author":"Turinici","year":"2014","journal-title":"Handbook of Functional Equations"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"259768","DOI":"10.1155\/2014\/259768","article-title":"Discussion on generalized-(\u03b1\u03c8 \u2212 \u03b2\u03d5)-contractive mappings via generalized altering distance function and related fixed point theorems","volume":"2014","author":"Berzig","year":"2014","journal-title":"Abstr. Appl. Anal."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1799","DOI":"10.1016\/j.na.2010.10.052","article-title":"Some fixed point generalizations are not real generalizations","volume":"74","author":"Haghi","year":"2011","journal-title":"Nonlinear Anal."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/2\/434\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:25:30Z","timestamp":1760120730000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/2\/434"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,6]]},"references-count":43,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,2]]}},"alternative-id":["sym15020434"],"URL":"https:\/\/doi.org\/10.3390\/sym15020434","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2023,2,6]]}}}