{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T11:35:15Z","timestamp":1771673715713,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,12,19]],"date-time":"2019-12-19T00:00:00Z","timestamp":1576713600000},"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"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The concept of symmetry is inherent in the study of metric spaces due to the presence of the symmetric property of the metric. Significant results, such as with the Borsuk\u2013Ulam theorem, make use of fixed-point arguments in their proofs to deal with certain symmetry principles. As such, the study of fixed-point results in metric spaces is highly correlated with the symmetry concept. In the current paper, we first define a new and modified \u0106iri\u0107-Reich\u2013Rus-type contraction in a b-metric space by incorporating the constant s in its definition and establish the corresponding fixed-point result. Next, we adopt an interpolative approach to establish some more fixed-point theorems. Existence of fixed points for    \u03c9   -interpolative \u0106iri\u0107-Reich\u2013Rus-type contractions are investigated in this context. We also illustrate the validity of our results with some examples.<\/jats:p>","DOI":"10.3390\/sym12010012","type":"journal-article","created":{"date-parts":[[2019,12,23]],"date-time":"2019-12-23T03:23:12Z","timestamp":1577071392000},"page":"12","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Fixed-Points of Interpolative \u0106iri\u0107-Reich\u2013Rus-Type Contractions in b-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":[[2019,12,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"133","DOI":"10.4064\/fm-3-1-133-181","article-title":"Sur les operationes dans les ensembles abstraits et leur application aux equqation integrales","volume":"3","author":"Banach","year":"1922","journal-title":"Fundam. 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