{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T15:12:52Z","timestamp":1746803572219,"version":"3.40.5"},"reference-count":26,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>Stability of iterative roots is important in their numerical computation. It is known that under some conditions iterative roots of orientation-preserving self-mappings are both globally<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:msup><mml:mrow><mml:mi>C<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>0<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math>stable and locally<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:msup><mml:mrow><mml:mi>C<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>1<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math>stable but globally<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:msup><mml:mrow><mml:mi>C<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>1<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math>unstable. Although the global<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:msup><mml:mrow><mml:mi>C<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>1<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math>instability implies the general global<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mrow><mml:msup><mml:mrow><mml:mi>C<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>r<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math>(<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:mi>r<\/mml:mi><mml:mo>\u2265<\/mml:mo><mml:mn>2<\/mml:mn><\/mml:math>) instability, the local<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\"><mml:mrow><mml:msup><mml:mrow><mml:mi>C<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>1<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math>stability does not guarantee the local<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M9\"><mml:mrow><mml:msup><mml:mrow><mml:mi>C<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>r<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math>(<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M10\"><mml:mi>r<\/mml:mi><mml:mo>\u2265<\/mml:mo><mml:mn>2<\/mml:mn><\/mml:math>) stability. In this paper we generally prove the local<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M11\"><mml:mrow><mml:msup><mml:mrow><mml:mi>C<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>r<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math>(<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M12\"><mml:mi>r<\/mml:mi><mml:mo>\u2265<\/mml:mo><mml:mn>2<\/mml:mn><\/mml:math>) stability for iterative roots. For this purpose we need a uniform estimate for the approximation to the conjugation in<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M13\"><mml:mrow><mml:msup><mml:mrow><mml:mi>C<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>r<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math>linearization, which is given by improving the method used for the<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M14\"><mml:mrow><mml:msup><mml:mrow><mml:mi>C<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>1<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math>case.<\/jats:p>","DOI":"10.1155\/2014\/743032","type":"journal-article","created":{"date-parts":[[2014,5,21]],"date-time":"2014-05-21T21:12:19Z","timestamp":1400706739000},"page":"1-8","source":"Crossref","is-referenced-by-count":0,"title":["Local<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:msup><mml:mrow><mml:mi>C<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>r<\/mml:mi><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math>Stability for Iterative Roots of Orientation-Preserving Self-Mappings on the Interval"],"prefix":"10.1155","volume":"2014","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5225-9642","authenticated-orcid":true,"given":"Yingying","family":"Zeng","sequence":"first","affiliation":[{"name":"Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China"}]}],"member":"311","reference":[{"key":"2","doi-asserted-by":"publisher","DOI":"10.1098\/rstl.1815.0024"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1955-0080911-2"},{"year":"1982","key":"19","first-page":"xii+198"},{"volume":"6","first-page":"292","year":"1981","key":"21"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1007\/s000100050159"},{"volume":"46","year":"1968","series-title":"Monograph in Mathematics","key":"11"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139086639"},{"issue":"5","key":"24","first-page":"385","volume":"24","year":"1995","journal-title":"Advances in Mathematics"},{"issue":"1","key":"4","first-page":"3","volume":"60","year":"1991","journal-title":"Acta Mathematica Universitatis Comenianae"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2011.08.033"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2011.01.037"},{"issue":"3-4","key":"5","doi-asserted-by":"crossref","first-page":"363","DOI":"10.5486\/PMD.1999.2080","volume":"55","year":"1999","journal-title":"Publicationes Mathematicae Debrecen"},{"issue":"2","key":"23","first-page":"203","volume":"48","year":"2000","journal-title":"Bulletin of the Polish Academy of Sciences. 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