{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:47:57Z","timestamp":1760237277784,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,3,21]],"date-time":"2020-03-21T00:00:00Z","timestamp":1584748800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Institute of Research and Development of Processes, University of the Basque Country, Campus of Leioa, Leioa (Bizkaia), PO BOX 48940, Spain","award":["IT1207-19"],"award-info":[{"award-number":["IT1207-19"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this work, we define the concept of a generalized c-distance in cone b-metric spaces over a Banach algebra and introduce some its properties. Then, we prove the existence and uniqueness of fixed points for mappings satisfying weak contractive conditions such as Han\u2013Xu-type contraction and Cho-type contraction with respect to this distance. Our assertions are useful, since we remove the continuity condition of the mapping and the normality condition for the cone. Several examples are given to support the main results.<\/jats:p>","DOI":"10.3390\/axioms9010031","type":"journal-article","created":{"date-parts":[[2020,3,23]],"date-time":"2020-03-23T04:03:01Z","timestamp":1584936181000},"page":"31","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Fixed Point Results under Generalized c-Distance in Cone b-Metric Spaces Over Banach Algebras"],"prefix":"10.3390","volume":"9","author":[{"given":"Ataollah","family":"Arabnia Firozjah","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, Tehra P. O. Box 13185\/768, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hamidreza","family":"Rahimi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, Tehra P. O. Box 13185\/768, Iran"}],"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 IIDP, Campus of Leioa, University of the Basque Country, PO BOX 48940 Leioa, Bizkaia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0758-2758","authenticated-orcid":false,"given":"Ghasem","family":"Soleimani Rad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, Tehra P. O. Box 13185\/768, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,21]]},"reference":[{"key":"ref_1","first-page":"211","article-title":"On some common fixed point theorems with rational expressions on cone metric spaces over a Banach algebra","volume":"41","year":"2012","journal-title":"Hacettepe J. Math. Stat."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1186\/1687-1812-2013-320","article-title":"Cone metric spaces with Banach algebras and fixed point theorems of generalized Lipschitz mappings","volume":"2013","author":"Liu","year":"2013","journal-title":"Fixed Point Theory Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1467","DOI":"10.1016\/j.jmaa.2005.03.087","article-title":"Cone metric spaces and fixed point theorems of contractive mappings","volume":"332","author":"Huang","year":"2007","journal-title":"J. Math. Anal. 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