{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T00:33:49Z","timestamp":1760402029560,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,1,8]],"date-time":"2020-01-08T00:00:00Z","timestamp":1578441600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003086","name":"Basque Government","doi-asserted-by":"publisher","award":["IT 1207-19"],"award-info":[{"award-number":["IT 1207-19"]}],"id":[{"id":"10.13039\/501100003086","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The symmetry concept is an intrinsic property of metric spaces as the metric function generalizes the notion of distance between two points. There are several remarkable results in science in connection with symmetry principles that can be proved using fixed point arguments. Therefore, fixed point theory and symmetry principles bear significant correlation between them. In this paper, we introduce the new definition of the eventually    \u0394   -restrictive set-valued map together with the concept of p-orbital continuity. Further, we introduce another new concept called the     \u0394 ( \u03f5 )    -restrictive set-valued map. We establish several fixed point results related to these maps and proofs of these results also provide us with schemes to find a fixed point. In a couple of results, the stronger condition of compactness of the underlying metric space is assumed. Some results are illustrated with examples.<\/jats:p>","DOI":"10.3390\/sym12010127","type":"journal-article","created":{"date-parts":[[2020,1,9]],"date-time":"2020-01-09T03:07:11Z","timestamp":1578539231000},"page":"127","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Fixed Points of Eventually \u0394-Restrictive and \u0394(\u03f5)-Restrictive Set-Valued Maps in Metric Spaces"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0097-0819","authenticated-orcid":false,"given":"Pradip","family":"Debnath","sequence":"first","affiliation":[{"name":"Department of Applied Science and Humanities, Assam University, Silchar, Cachar, Assam 788011, India"}]},{"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, University of the Basque Country, Campus of Leioa, 48940 Leioa (Bizakaia), Spain"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1090\/S0002-9904-1968-11971-8","article-title":"A fixed point theorem for set- valued mappings","volume":"74","author":"Markin","year":"1968","journal-title":"Bull. Am. Math. Soc."},{"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","doi-asserted-by":"crossref","first-page":"553","DOI":"10.2140\/pjm.1972.43.553","article-title":"Fixed point theorems for set-valued mappings of contractive type","volume":"43","author":"Assad","year":"1972","journal-title":"Pac. J. Math."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Jleli, M., Samet, B., Vetro, C., and Vetro, F. (2015). Fixed points for multivalued mappings in b-metric spaces. Abstr. Appl. Anal., 718074.","DOI":"10.1186\/s13663-015-0293-6"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Kirk, W.A., and Shahzad, N. (2014). Fixed Point Theory in Distance Spaces, Springer.","DOI":"10.1007\/978-3-319-10927-5"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2499","DOI":"10.2298\/FIL1708499C","article-title":"Fixed point results for multivalued Hardy-Rogers contractions in b-metric spaces","volume":"31","author":"Chifu","year":"2017","journal-title":"Filomat"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Qawaqneh, H., Noorani, M.S.M., Shatanawi, W., and Aydi, H. (2019). Fixed point results for multi-valued contractions in b-metric spaces and an application. Mathematics, 7.","DOI":"10.3390\/math7020132"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Pathak, H.K. (2018). An Introduction to Nonlinear Analysis and Fixed Point Theory, Springer.","DOI":"10.1007\/978-981-10-8866-7"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Debnath, P., and de La Sen, M. (2019). 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Appl."},{"key":"ref_18","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. Lond. Math. Soc."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1017\/S0305004100037956","article-title":"On non-expansive mappings of Banach spaces","volume":"60","author":"Edelstein","year":"1964","journal-title":"Proc. Camb. Philos. Soc."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Aydi, H., Bankovi\u0107, R., Mitrovi\u0107, I., and Nazam, M. (2018). Nemytzki-Edelstein-Meir-Keeler type results in b-metric spaces. Discret. Dyn. Nat. Soc., 4745764.","DOI":"10.1155\/2018\/4745764"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1112\/jlms\/s1-41.1.101","article-title":"Some theorems on contractive mappings","volume":"41","author":"Bailey","year":"1966","journal-title":"J. Lond. Math. Soc."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/1\/127\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:19:14Z","timestamp":1760361554000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/1\/127"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,8]]},"references-count":21,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,1]]}},"alternative-id":["sym12010127"],"URL":"https:\/\/doi.org\/10.3390\/sym12010127","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2020,1,8]]}}}