{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:11:58Z","timestamp":1760145118197,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,6,20]],"date-time":"2024-06-20T00:00:00Z","timestamp":1718841600000},"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>In this manuscript, we prove numerous results concerning fixed points, common fixed points, coincidence points, coupled coincidence points, and coupled common fixed points for (\u03d5,\u03a8)-contractive mappings in the framework of partially ordered controlled metric spaces. Our findings introduce a novel perspective on this mathematical context, and we illustrate the uniqueness of our findings through various explanatory examples. Also, we apply the main result to find the existence and uniqueness of the solution of the system of integral equations as an application.<\/jats:p>","DOI":"10.3390\/axioms13060415","type":"journal-article","created":{"date-parts":[[2024,6,21]],"date-time":"2024-06-21T03:44:49Z","timestamp":1718941489000},"page":"415","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Fixed-Point Results of Generalized (\u03d5,\u03a8)-Contractive Mappings in Partially Ordered Controlled Metric Spaces with an Application to a System of Integral Equations"],"prefix":"10.3390","volume":"13","author":[{"given":"Mohammad","family":"Akram","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia"}]},{"given":"Salha","family":"Alshaikey","sequence":"additional","affiliation":[{"name":"Mathematics Department, Al-Qunfudah University College, Umm Al-Qura University, Mecca 24382, Saudi Arabia"}]},{"given":"Umar","family":"Ishtiaq","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan"}]},{"given":"Muhammad","family":"Farhan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, National University of Modern Languages Islamabad, Multan Campus, Multan 59300, Pakistan"}]},{"given":"Ioannis K.","family":"Argyros","sequence":"additional","affiliation":[{"name":"Department of Computing and Mathematical Sciences, Cameron University, Lawton, OK 73505, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0035-1022","authenticated-orcid":false,"given":"Samundra","family":"Regmi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Houston, Houston, TX 77204, USA"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,20]]},"reference":[{"key":"ref_1","first-page":"5","article-title":"Contraction mappings in b-metric spaces","volume":"1","author":"Czerwik","year":"1993","journal-title":"Acta Math. Inform. Univ. Ostrav."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Mlaiki, N., Dedovic, N., Aydi, H., Garda\u0161evi\u0107-Filipovi\u0107, M., Bin-Mohsin, B., and Radenovi\u0107, S. (2019). Some new observations on Geraghty and \u0106iri\u0107 type results in b-metric spaces. Mathematics, 7.","DOI":"10.3390\/math7070643"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Faraji, H., Savi\u0107, D., and Radenovi\u0107, S. (2019). Fixed point theorems for Geraghty contraction type mappings in b-metric spaces and applications. Axioms, 8.","DOI":"10.3390\/axioms8010034"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"438","DOI":"10.5937\/vojtehg68-26718","article-title":"Solutions and Ulam-Hyers stability of differential inclusions involving Suzuki type multivalued mappings on b-metric spaces","volume":"68","author":"Abas","year":"2020","journal-title":"Vojnotehni\u010dki Glasnik\/Military Technical Courier"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3815","DOI":"10.22436\/jnsa.010.07.35","article-title":"On multi-valued weak quasi-contractions in b-metric spaces","volume":"10","author":"Hussain","year":"2017","journal-title":"J. Nonlinear Sci. Appl."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1515\/ms-2017-0217","article-title":"Common fixed point theorems for a class of (s,q)-contractive mappings in b-metric-like spaces and applications to integral equations","volume":"69","author":"Zoto","year":"2019","journal-title":"Math. Slovaca"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"256","DOI":"10.1186\/s13660-017-1528-3","article-title":"Basic inequality on a b-metric space and its applications","volume":"2017","author":"Suzuki","year":"2017","journal-title":"J. Inequalities Appl."},{"key":"ref_8","first-page":"401","article-title":"Coincidences and Fixed Points of Hybrid Contractions","volume":"24","author":"Singh","year":"2008","journal-title":"Tamsui Oxf. J. Math. Sci. (TOJMS)"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Mlaiki, N., Aydi, H., Souayah, N., and Abdeljawad, T. (2018). Controlled metric type spaces and the related contraction principle. Mathematics, 6.","DOI":"10.3390\/math6100194"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1435","DOI":"10.1090\/S0002-9939-03-07220-4","article-title":"A fixed point theorem in partially ordered sets and some applications to matrix equations","volume":"132","author":"Ran","year":"2004","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2238","DOI":"10.1016\/j.na.2009.10.023","article-title":"A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations","volume":"72","author":"Emami","year":"2010","journal-title":"Nonlinear Anal. Theory Methods Appl."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Farhan, M., Ishtiaq, U., Saeed, M., Hussain, A., and Al Sulami, H. (2022). Reich-Type and (\u03b1,F)-Contractions in Partially Ordered Double-Controlled Metric-Type Spaces with Applications to Non-Linear Fractional Differential Equations and Monotonic Iterative Method. Axioms, 11.","DOI":"10.3390\/axioms11100573"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1379","DOI":"10.1016\/j.na.2005.10.017","article-title":"Fixed point theorems in partially ordered metric spaces and applications","volume":"65","author":"Bhaskar","year":"2006","journal-title":"Nonlinear Anal. Theory Methods Appl."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4341","DOI":"10.1016\/j.na.2008.09.020","article-title":"Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces","volume":"70","author":"Lakshmikantham","year":"2009","journal-title":"Nonlinear Anal. Theory Methods Appl."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11565-011-0117-5","article-title":"Coupled coincidence point theorems in ordered metric spaces","volume":"57","author":"Choudhury","year":"2011","journal-title":"Annali Dell\u2019Universita\u2019Di Ferrara"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Mitiku, B., Karusala, K., and Namana, S.R. (2020). Some fixed point results of generalized (\u03d5,\u03c8)-contractive mappings in ordered b-metric spaces. BMC Res. Notes, 13.","DOI":"10.1186\/s13104-020-05354-1"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2205","DOI":"10.1007\/s10114-005-0769-0","article-title":"Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations","volume":"23","author":"Nieto","year":"2007","journal-title":"Acta Math. Sin. Engl. Ser."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1186\/1687-1812-2012-101","article-title":"Tripled coincidence point results for generalized contractions in ordered generalized metric spaces","volume":"2012","author":"Aydi","year":"2012","journal-title":"Fixed Point Theory Appl."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1186\/1687-1812-2013-130","article-title":"Existence of tripled coincidence points in ordered b-metric spaces and an application to a system of integral equations","volume":"2013","author":"Parvaneh","year":"2013","journal-title":"Fixed Point Theory Appl."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Ishtiaq, U., Kattan, D.A., Ahmad, K., Sessa, S., and Ali, F. (2023). Fixed point results in controlled fuzzy metric spaces with an application to the transformation of solar energy to electric power. Mathematics, 15.","DOI":"10.3390\/math11153435"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1016\/j.jmaa.2018.07.022","article-title":"A fixed point theorem and the Ulam stability in generalized dq-metric spaces","volume":"467","year":"2018","journal-title":"J. Math. Anal. Appl."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"501","DOI":"10.2989\/16073606.2023.2229559","article-title":"Fixed points of principal E 6-bundles over a compact algebraic curve","volume":"47","year":"2024","journal-title":"Quaest. Math."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1007\/s00009-023-02559-z","article-title":"Fixed Points of Automorphisms of the Vector Bundle Moduli Space Over a Compact Riemann Surface","volume":"21","year":"2024","journal-title":"Mediterr. J. Math."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/6\/415\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:01:59Z","timestamp":1760108519000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/6\/415"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,20]]},"references-count":23,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2024,6]]}},"alternative-id":["axioms13060415"],"URL":"https:\/\/doi.org\/10.3390\/axioms13060415","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2024,6,20]]}}}