{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:29:11Z","timestamp":1760149751801,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,9,13]],"date-time":"2023-09-13T00:00:00Z","timestamp":1694563200000},"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 2007, in our joint work with D. Butnariu and S. Reich, we proved that if for a self-mapping of a complete metric that is uniformly continuous on bounded sets all its iterates converge uniformly on bounded sets, then this convergence is stable under the presence of small errors. In the present paper, we obtain an extension of this result for self-mappings of a metric space with a graph.<\/jats:p>","DOI":"10.3390\/sym15091756","type":"journal-article","created":{"date-parts":[[2023,9,14]],"date-time":"2023-09-14T09:57:56Z","timestamp":1694685476000},"page":"1756","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Three Convergence Results for Iterates of Nonlinear Mappings in Metric Spaces with Graphs"],"prefix":"10.3390","volume":"15","author":[{"given":"Alexander J.","family":"Zaslavski","sequence":"first","affiliation":[{"name":"Department of Mathematics, The Technion\u2014Israel Institute of Technology, Haifa 32000, Israel"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1007\/s41478-020-00248-8","article-title":"Some Caristi type fixed point theorems","volume":"29","author":"Aslantas","year":"2021","journal-title":"J. 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