{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T22:38:59Z","timestamp":1768516739689,"version":"3.49.0"},"reference-count":9,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,9,3]],"date-time":"2021-09-03T00:00:00Z","timestamp":1630627200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We point out a vital error in the paper of Gaba et al. (2019), showing that a (\u03c1,\u03b7,\u03bc) interpolative Kannan contraction in a complete metric space need not have a fixed point. Then we give an appropriate restriction on a (\u03c1,\u03b7,\u03bc)-interpolative Kannan contraction that guarantees the existence of a fixed point and provide an equivalent formulation. Moreover, we show that this formulation can be extended to the interpolative Reich-Rus-\u0106iri\u0107 type contraction.<\/jats:p>","DOI":"10.3390\/axioms10030212","type":"journal-article","created":{"date-parts":[[2021,9,6]],"date-time":"2021-09-06T13:09:25Z","timestamp":1630933765000},"page":"212","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["(\u03c1,\u03b7,\u03bc)-Interpolative Kannan Contractions I"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8128-9704","authenticated-orcid":false,"given":"Ya\u00e9 Ulrich","family":"Gaba","sequence":"first","affiliation":[{"name":"Institut de Math\u00e9matiques et de Sciences Physiques (IMSP\/UAC), Laboratoire de Topologie Fondamentale, Computationnelle et leurs Applications (Lab-ToFoCApp), Porto-Novo BP 613, Benin"},{"name":"African Center for Advanced Studies (ACAS), P.O. Box 4477, Yaounde 7535, Cameroon"},{"name":"Quantum Leap Africa (QLA), AIMS Rwanda Centre, Remera Sector, Kigali KN 3, Rwanda"},{"name":"Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, P.O. Box 60, Ga-Rankuwa 0208, South Africa"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4606-7211","authenticated-orcid":false,"given":"Hassen","family":"Aydi","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, P.O. Box 60, Ga-Rankuwa 0208, South Africa"},{"name":"Institut Sup\u00e9rieur d\u2019Informatique et des Techniques de Communication, Universit\u00e9 de Sousse, H. Sousse 4000, Tunisia"},{"name":"China Medical University Hospital, China Medical University, Taichung 40402, Taiwan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7986-886X","authenticated-orcid":false,"given":"Nabil","family":"Mlaiki","sequence":"additional","affiliation":[{"name":"Department of Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,3]]},"reference":[{"key":"ref_1","first-page":"71","article-title":"Some results on fixed points","volume":"60","author":"Kannan","year":"1968","journal-title":"Bull. Calcutta Math. Soc."},{"key":"ref_2","first-page":"85","article-title":"Revisiting the Kannan type contractions via interpolation","volume":"2","author":"Karapinar","year":"2018","journal-title":"Adv. Theory Nonlinear Anal. Appl."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Aydi, H., Chen, C.M., and Karapinar, E. (2019). Interpolative Ciric-Reich-Rus type contractions via the Branciari distance. Mathematics, 7.","DOI":"10.3390\/math7010084"},{"key":"ref_4","first-page":"2075920","article-title":"Some remarks on fixed point theorems for interpolative Kannan contraction","volume":"2020","author":"Errai","year":"2020","journal-title":"J. Funct. Spaces"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Karapinar, E., Alqahtani, O., and Aydi, H. (2019). On interpolative Hardy-Rogers type contractions. Symmetry, 11.","DOI":"10.3390\/sym11010008"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Gaba, Y.U., and Karapinar, E. (2019). A new approach to the interpolative contractions. Axioms, 8.","DOI":"10.3390\/axioms8040110"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Aydi, H., Karapinar, E., and de Hierro Francisco, R.L. (2019). \u03c9-Interpolative Ciric-Reich-Rus type contractions. Mathematics, 7.","DOI":"10.3390\/math7010057"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Debnath, P., and de La Sen, M. (2020). Fixed-points of interpolative \u0106iri\u0107-Reich-Rus-type contractions in metric spaces. Symmetry, 12.","DOI":"10.3390\/sym12010012"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Karapinar, E., Agarwal, R.P., and Aydi, H. (2018). Interpolative Reich-Rus-\u0106iri\u0107 type contractions on partial metric spaces. Mathematics, 6.","DOI":"10.3390\/math6110256"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/10\/3\/212\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:55:23Z","timestamp":1760165723000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/10\/3\/212"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,3]]},"references-count":9,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,9]]}},"alternative-id":["axioms10030212"],"URL":"https:\/\/doi.org\/10.3390\/axioms10030212","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,9,3]]}}}