{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T12:30:14Z","timestamp":1770813014848,"version":"3.50.1"},"reference-count":91,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,6,20]],"date-time":"2022-06-20T00:00:00Z","timestamp":1655683200000},"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>We present a survey of the theory of measures of noncompactness and discuss some fixed point theorems of Darbo\u2019s type. We apply the technique of measures of noncompactness to the characterization of classes of compact operators between certain sequence spaces, in solving infinite systems of integral equations in some sequence spaces. We also present some recent results related to the existence of best proximity points (pairs) for some classes of cyclic and noncyclic condensing operators in Banach spaces equipped with a suitable measure of noncompactness. Finally, we discuss the existence of an optimal solution for systems of integro\u2013differentials.<\/jats:p>","DOI":"10.3390\/axioms11060299","type":"journal-article","created":{"date-parts":[[2022,6,21]],"date-time":"2022-06-21T01:43:27Z","timestamp":1655775807000},"page":"299","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["A New Survey of Measures of Noncompactness and Their Applications"],"prefix":"10.3390","volume":"11","author":[{"given":"Moosa","family":"Gabeleh","sequence":"first","affiliation":[{"name":"Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd RQHV3W6, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eberhard","family":"Malkowsky","sequence":"additional","affiliation":[{"name":"Department of Mathematics, State University of Novi Pazar, Vuka Karad\u017ei\u0107a bb, 36300 Novi Pazar, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4128-0427","authenticated-orcid":false,"given":"Mohammad","family":"Mursaleen","sequence":"additional","affiliation":[{"name":"Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), No. 91, Xueshi Rd, North District, Taichung City 404, Taiwan"},{"name":"Department of Mathematics, Aligarh Muslim University, Aligarh 202002, UP, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vladimir","family":"Rako\u010devi\u0107","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences and Mathematics, University of Ni\u0161, Vi\u0161egradska 33, 18000 Ni\u0161, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"301","DOI":"10.4064\/fm-15-1-301-309","article-title":"Sur les espaces complets","volume":"15","author":"Kuratowski","year":"1930","journal-title":"Fund. 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