{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:46:07Z","timestamp":1760237167180,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,3,4]],"date-time":"2020-03-04T00:00:00Z","timestamp":1583280000000},"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":["Grant IT 1207-19"],"award-info":[{"award-number":["Grant IT 1207-19"]}],"id":[{"id":"10.13039\/501100003086","id-type":"DOI","asserted-by":"publisher"}]},{"name":"UGC India","award":["F.30-452\/2018(BSR)"],"award-info":[{"award-number":["F.30-452\/2018(BSR)"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The symmetry concept is a congenital characteristic of the metric function. In this paper, our primary aim is to study the fixed points of a broad category of set-valued maps which may include discontinuous maps as well. To achieve this objective, we newly extend the notions of orbitally continuous and asymptotically regular mappings in the set-valued context. We introduce two new contractive inequalities one of which is of Geraghty-type and the other is of Boyd and Wong-type. We proved two new existence of fixed point results corresponding to those inequalities.<\/jats:p>","DOI":"10.3390\/sym12030411","type":"journal-article","created":{"date-parts":[[2020,3,4]],"date-time":"2020-03-04T10:46:08Z","timestamp":1583318768000},"page":"411","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Contractive Inequalities for Some Asymptotically Regular Set-Valued Mappings and Their Fixed Points"],"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"}],"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, University of the Basque Country, Campus of Leioa, 48940 Leioa (Bizakaia), Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,4]]},"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","first-page":"718074","DOI":"10.1155\/2015\/718074","article-title":"Fixed points for multivalued mappings in b-metric spaces","volume":"2015","author":"Jleli","year":"2015","journal-title":"Abstr. Appl. Anal."},{"key":"ref_5","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_6","doi-asserted-by":"crossref","unstructured":"Debnath, P., and de La Sen, M. (2019). Set-valued interpolative Hardy-Rogers and set-valued Reich-Rus-Ciric-type contractions in b-metric spaces. Mathematics, 7.","DOI":"10.3390\/math7090849"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Bucur, A. (2020). Fixed Points for Multivalued Weighted Mean Contractions in a Symmetric Generalized Metric Space. Symmetry, 12.","DOI":"10.3390\/sym12010134"},{"key":"ref_8","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_9","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_10","first-page":"65","article-title":"Fixed point theorems for some multivalued generalized contraction in b-metric spaces","volume":"6","author":"Boriceanu","year":"2010","journal-title":"Int. J. Math. Stat."},{"key":"ref_11","first-page":"263","article-title":"Nonlinear set-valued contraction mappings in b-metric spaces","volume":"46","author":"Czerwik","year":"1998","journal-title":"Atti Sem. Mat. Univ. Modena"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Debnath, P., and de La Sen, M. (2020). Fixed points of eventually \u0394-restrictive and \u0394(\u03f5)-restrictive set-valued maps in metric spaces. Symmetry, 12.","DOI":"10.3390\/sym12010127"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"772","DOI":"10.1016\/j.jmaa.2006.03.016","article-title":"On a general class of multi-valued weakly picard mappings","volume":"326","author":"Berinde","year":"2007","journal-title":"J. Math. Anal. Appl."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1006\/jmaa.1995.1194","article-title":"Fixed points of generalized contractive multi-valued mappings","volume":"192","author":"Daffer","year":"1995","journal-title":"J. Math. Anal. Appl."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1090\/S0002-9947-1977-0433430-4","article-title":"A comparison of various definitions of contractive mappings","volume":"226","author":"Rhoades","year":"1977","journal-title":"Trans. Am. Math. Soc."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/s11784-019-0668-0","article-title":"Remarks on asymptotic regularity and fixed points","volume":"21","year":"2019","journal-title":"J. Fixed Point Theory Appl."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1006\/jmaa.1999.6560","article-title":"Discontinuity and fixed points","volume":"240","author":"Pant","year":"1999","journal-title":"J. Math. Anal. Appl."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1007\/s11784-019-0695-x","article-title":"A note on the fixed point theorem of G\u00f3rnicki","volume":"21","author":"Bisht","year":"2019","journal-title":"J. Fixed Point Theory Appl."},{"key":"ref_19","first-page":"284","article-title":"Fixed points of asymptotically regular multivalued mappings","volume":"53","author":"Beg","year":"1992","journal-title":"J. Aust. Math. Soc. (Ser. A)"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3299","DOI":"10.1016\/j.na.2009.01.212","article-title":"New fixed point theorems for asymptotically regular multi-valued maps","volume":"71","author":"Singh","year":"2009","journal-title":"Nonlinear Anal."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1007\/s11784-019-0741-8","article-title":"On some mappings with a unique fixed point","volume":"22","year":"2020","journal-title":"J. Fixed Point Theory Appl."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"604","DOI":"10.1090\/S0002-9939-1973-0334176-5","article-title":"On contractive mappings","volume":"40","author":"Geraghty","year":"1973","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"458","DOI":"10.1090\/S0002-9939-1969-0239559-9","article-title":"On nonlinear contractions","volume":"20","author":"Boyd","year":"1969","journal-title":"Proc. Am. Math. 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