{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T04:48:44Z","timestamp":1782276524823,"version":"3.54.5"},"reference-count":35,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,7,4]],"date-time":"2023-07-04T00:00:00Z","timestamp":1688428800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we modify the KF-iteration process into hyperbolic metric spaces where the symmetry condition is satisfied and establish the weak w2-stability and data dependence results for contraction mappings. We also prove some \u0394-convergence and strong convergence theorems for generalized (\u03b1,\u03b2)-nonexpansive type 1 mappings. Finally, we offer a numerical example of generalized (\u03b1,\u03b2)-nonexpansive type 1 mappings and show that the KF-iteration process is more effective than some other iterations. Our results generalize and improve several relevant results in the literature.<\/jats:p>","DOI":"10.3390\/sym15071360","type":"journal-article","created":{"date-parts":[[2023,7,5]],"date-time":"2023-07-05T00:33:42Z","timestamp":1688517222000},"page":"1360","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Some Fixed-Point Results for the KF-Iteration Process in Hyperbolic Metric Spaces"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6114-9966","authenticated-orcid":false,"given":"Aynur","family":"\u015eahin","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, Sakarya University, Serdivan 54050, T\u00fcrkiye"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5427-534X","authenticated-orcid":false,"given":"Emre","family":"\u00d6zt\u00fcrk","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, Sakarya University, Serdivan 54050, T\u00fcrkiye"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5890-0920","authenticated-orcid":false,"given":"Gaurav","family":"Aggarwal","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Jaypee Institute of Information Technology, Noida 201309, India"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"506","DOI":"10.1090\/S0002-9939-1953-0054846-3","article-title":"Mean value methods in iteration","volume":"4","author":"Mann","year":"1953","journal-title":"Proc. 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