{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T11:07:11Z","timestamp":1772536031309,"version":"3.50.1"},"reference-count":42,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,7,26]],"date-time":"2021-07-26T00:00:00Z","timestamp":1627257600000},"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>The purpose of this paper is to introduce the class of enriched multivalued contraction mappings. Both single-valued and multivalued enriched contractions are defined by means of symmetric inequalities. Our main result extends and generalizes the recent result of Berinde and P\u0103curar (Approximating fixed points of enriched contractions in Banach spaces, Journal of Fixed Point Theory and Applications, 22 (2), 1\u201310, 2020). We also study a data dependence problem of the fixed point set and Ulam\u2013Hyers stability of the fixed point problem for enriched multivalued contraction mappings. Applications of the results obtained to the problem of the existence of a solution of differential inclusions and dynamic programming are presented.<\/jats:p>","DOI":"10.3390\/sym13081350","type":"journal-article","created":{"date-parts":[[2021,7,26]],"date-time":"2021-07-26T09:25:52Z","timestamp":1627291552000},"page":"1350","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["Enriched Multivalued Contractions with Applications to Differential Inclusions and Dynamic Programming"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5528-1207","authenticated-orcid":false,"given":"Mujahid","family":"Abbas","sequence":"first","affiliation":[{"name":"Department of Mathematics, Government College University, Katchery Road, Lahore 54000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2864-6730","authenticated-orcid":false,"given":"Rizwan","family":"Anjum","sequence":"additional","affiliation":[{"name":"Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3677-795X","authenticated-orcid":false,"given":"Vasile","family":"Berinde","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, North University Center at Baia Mare, Technical University of Cluj-Napoca, Victoriei 76, 430122 Baia Mare, Romania"},{"name":"Academy of Romanian Scientists, Ilfov Str. No. 3, 50044 Bucharest, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"133","DOI":"10.4064\/fm-3-1-133-181","article-title":"Sur les op\u00e9rations dans les ensembles abstraits et leurs applications aux \u00e9quations int\u00e9grales","volume":"3","author":"Banach","year":"1922","journal-title":"Fund. Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"475","DOI":"10.2140\/pjm.1969.30.475","article-title":"Multi-valued contraction mappings","volume":"30","author":"Nadler","year":"1969","journal-title":"Pac. J. Math."},{"key":"ref_3","first-page":"35","article-title":"The role of the Pompeiu-Hausdorff metric in fixed point theory","volume":"22","author":"Berinde","year":"2013","journal-title":"Creat. Math. 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