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We establish a convergence condition in the form of escape criterion which allows to adapt the escape-time algorithm to the considered iteration scheme. We also present some graphical examples of the Mandelbrot and Julia fractals showing the dependency of Julia and Mandelbrot sets on complex polynomials, contraction mappings, and iteration parameters. Moreover, we propose two numerical measures that allow the study of the dependency of the set shape change on the values of the iteration parameters. Using these two measures, we show that the dependency for the considered iteration method is non-linear.<\/jats:p>","DOI":"10.1007\/s11075-023-01644-4","type":"journal-article","created":{"date-parts":[[2023,8,17]],"date-time":"2023-08-17T11:02:40Z","timestamp":1692270160000},"page":"211-236","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":30,"title":["On the viscosity approximation type iterative method and its non-linear behaviour in the generation of Mandelbrot and Julia sets"],"prefix":"10.1007","volume":"96","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0498-5268","authenticated-orcid":false,"given":"Sudesh","family":"Kumari","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9434-9307","authenticated-orcid":false,"given":"Krzysztof","family":"Gdawiec","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ashish","family":"Nandal","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Naresh","family":"Kumar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Renu","family":"Chugh","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,8,17]]},"reference":[{"key":"1644_CR1","doi-asserted-by":"publisher","unstructured":"Agarwal, S.: Cryptographic key generation using burning ship fractal. 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