{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T16:39:35Z","timestamp":1778776775509,"version":"3.51.4"},"reference-count":43,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,4,22]],"date-time":"2021-04-22T00:00:00Z","timestamp":1619049600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Basque Government","award":["Grant IT1207-19."],"award-info":[{"award-number":["Grant IT1207-19."]}]},{"name":"NBHM, DAE","award":["02011\/11\/2020\/NBHM (RP)\/R&D- II\/7830"],"award-info":[{"award-number":["02011\/11\/2020\/NBHM (RP)\/R&D- II\/7830"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In the present work, we consider the best proximal problem related to a coupled mapping, which we define using control functions and weak inequalities. As a consequence, we obtain some results on coupled fixed points. Our results generalize some recent results in the literature. Also, as an application of the results obtained, we present the solution to a system of a coupled Fredholm nonlinear integral equation. Our work is supported by several illustrations.<\/jats:p>","DOI":"10.3390\/axioms10020073","type":"journal-article","created":{"date-parts":[[2021,4,22]],"date-time":"2021-04-22T13:59:14Z","timestamp":1619099954000},"page":"73","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Coupled Optimal Results with an Application to Nonlinear Integral Equations"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0971-511X","authenticated-orcid":false,"given":"Pulak","family":"Konar","sequence":"first","affiliation":[{"name":"Department of Mathematics, Amity University, Kadampukur, 24PGS(N), Kolkata 700135, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1928-2952","authenticated-orcid":false,"given":"Sumit","family":"Chandok","sequence":"additional","affiliation":[{"name":"School of Mathematics, Thapar Institute of Engineering &amp; Technology, Patiala 147004, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shrutinil","family":"Dutta","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Amity University, Kadampukur, 24PGS(N), Kolkata 700135, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9320-9433","authenticated-orcid":false,"given":"Manuel","family":"De la Sen","sequence":"additional","affiliation":[{"name":"Institute of Research and Development of Processes IIDP, Campus of Leioa, University of the Basque Country, P.O. Box 48940 Leioa, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,4,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"133","DOI":"10.4064\/fm-3-1-133-181","article-title":"Sur l\u00e9s oprations dans l\u00e9s ensembles abstraits et leurs applications aux quations intgrales","volume":"3","author":"Banach","year":"1922","journal-title":"Fund. Math."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Kirk, W.A., and Sims, B. (2001). 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