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In particular, we give necessary and sufficient conditions under which a convex combination and composition of strict pseudocontractions as well as demicontractions that share a common fixed point is again a strict pseudocontraction or a demicontraction, respectively. Moreover, we introduce a generalized relaxation of composition of demicontraction and give its properties. We\u201c apply these properties to prove the weak convergence of a class of algorithms that is wider than the Douglas\u2013Rachford algorithm and projected Landweber algorithms. We have also presented two numerical examples, where we compare the behavior of the presented methods with the Douglas\u2013Rachford method.<\/jats:p>","DOI":"10.1007\/s11075-023-01623-9","type":"journal-article","created":{"date-parts":[[2023,9,1]],"date-time":"2023-09-01T07:02:34Z","timestamp":1693551754000},"page":"1611-1642","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Strict pseudocontractions and demicontractions, their properties, and applications"],"prefix":"10.1007","volume":"95","author":[{"given":"Andrzej","family":"Cegielski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,9,1]]},"reference":[{"key":"1623_CR1","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/s00186-019-00691-9","volume":"91","author":"FJ Arag\u00f3n Artacho","year":"2020","unstructured":"Arag\u00f3n Artacho, F.J., Campoy, R., Tam, M.K.: The Douglas-Rachford algorithm for convex and nonconvex feasibility problems. 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