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We apply this new iteration process to approximate fixed points of generalized <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\alpha $$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03b1<\/mml:mi>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula>\u2013nonexpansive mappings. Convergence analysis of our newly proposed iteration process is discussed in the setting of uniformly convex Banach spaces and results are correlated with some other existing iteration processes. The dominance of the newly proposed iteration process is exhibited with the help of a new numerical example. In the end, the comparison of polynomiographs generated by other well-known iteration processes with our proposed iteration process has been presented to make a strong impression of our proposed iteration process.<\/jats:p>","DOI":"10.1007\/s11075-024-01859-z","type":"journal-article","created":{"date-parts":[[2024,6,18]],"date-time":"2024-06-18T09:06:55Z","timestamp":1718701615000},"page":"1943-1964","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Convergence analysis of Picard\u2013SP iteration process for generalized $$\\alpha $$\u2013nonexpansive mappings"],"prefix":"10.1007","volume":"98","author":[{"given":"Bashir","family":"Nawaz","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kifayat","family":"Ullah","sequence":"additional","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"}]}],"member":"297","published-online":{"date-parts":[[2024,6,18]]},"reference":[{"issue":"2","key":"1859_CR1","first-page":"223","volume":"66","author":"M Abbas","year":"2014","unstructured":"Abbas, M., Nazir, T.: A new faster iteration process applied to constrained minimization and feasibility problems. 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