{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:40:15Z","timestamp":1760060415505,"version":"build-2065373602"},"reference-count":14,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,8,27]],"date-time":"2025-08-27T00:00:00Z","timestamp":1756252800000},"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>Let E and F be nonempty disjoint subsets of a metric space (M,d). For a non-self-mapping \u03c6:E\u2192F, which is fixed-point free, a point \u03f0\u2208E is said to be a best proximity point for the mapping \u03c6 whenever the distance of the point \u03f0 to its image under \u03c6 is equal to the distance between the sets, E and F. In this article, we establish new best proximity point theorems and obtain real extensions of Edelstein\u2019s fixed point theorem in metric spaces, Krasnoselskii\u2019s fixed point theorem in strictly convex Banach spaces, Dhage\u2019s fixed point theorem in strictly convex Banach algebras, and Sadovskii\u2019s fixed point problem in strictly convex Banach spaces. We then present applications of these best proximity point results to complex function theory, as well as the existence of a solution of a nonlinear functional integral equation and the existence of a mutually nearest solution for a system of integral equations.<\/jats:p>","DOI":"10.3390\/axioms14090657","type":"journal-article","created":{"date-parts":[[2025,8,27]],"date-time":"2025-08-27T08:19:32Z","timestamp":1756282772000},"page":"657","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Certain Novel Best Proximity Theorems with Applications to Complex Function Theory and Integral Equations"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5439-1631","authenticated-orcid":false,"given":"Moosa","family":"Gabeleh","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Basic Sciences, Ayatollah Boroujerdi University, Boroujerd 69199-69737, Iran"},{"name":"Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Pretoria 0204, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"171","DOI":"10.4064\/sm-2-1-171-180","article-title":"Der Fixpunktsatz in Funktionalriiumen","volume":"2","author":"Schauder","year":"1930","journal-title":"Studia Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1112\/jlms\/s1-37.1.74","article-title":"On fixed and periodic points under contractive mappings","volume":"37","author":"Edelstein","year":"1962","journal-title":"J. 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Anal."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"680","DOI":"10.1016\/j.indag.2017.02.004","article-title":"Markov\u2013Kakutani\u2019s theorem for best proximity pairs in Hadamard spaces","volume":"28","author":"Gabeleh","year":"2017","journal-title":"Indag. Math."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1007\/s10957-011-9869-4","article-title":"Best Proximity Points: Optimal Solutions","volume":"151","author":"Basha","year":"2011","journal-title":"J. Optim. Theory Appl."},{"key":"ref_9","first-page":"313","article-title":"Best proximity points for proximal contractions","volume":"15","year":"2014","journal-title":"J. Nonlin. Convex Anal."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Akhmerov, A.A., Kamenskii, M.I., Potapov, A.S., Rodkina, A.E., and Sadovski, B.N. (1992). Measure of Noncompactness and Condensing Operators, Springer.","DOI":"10.1007\/978-3-0348-5727-7"},{"key":"ref_11","first-page":"797","article-title":"On Darbo-Sadovskii\u2019s fixed point theorems type for abstract measures of (weak) noncompactness","volume":"24","author":"Latrach","year":"2015","journal-title":"Bull. Belgian Math. Soc. (Simon Stevin)"},{"key":"ref_12","first-page":"74","article-title":"On a fixed point principle","volume":"4","author":"Sadovskii","year":"1967","journal-title":"Funkt. Anal."},{"key":"ref_13","unstructured":"Gabeleh, M. (Rocky Mt. J. Math., 2025). Best proximity points of multiplication of two operators in strictly convex Banach algebras, Rocky Mt. J. Math., to appear."},{"key":"ref_14","first-page":"84","article-title":"Punti uniti in transformazioni a condomino non compatto","volume":"24","author":"Darbo","year":"1955","journal-title":"Rend. Sem. Mat. Uni. Padova"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/9\/657\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:33:25Z","timestamp":1760034805000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/9\/657"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,27]]},"references-count":14,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2025,9]]}},"alternative-id":["axioms14090657"],"URL":"https:\/\/doi.org\/10.3390\/axioms14090657","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2025,8,27]]}}}