{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:37:39Z","timestamp":1760143059382,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,1,16]],"date-time":"2024-01-16T00:00:00Z","timestamp":1705363200000},"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 this paper, we present a result on the existence of asymptotically stable solutions of infinite systems (IS) of quadratic Hammerstein integral equations (IEs). Our study will be conducted in the Banach space of functions, which are continuous and bounded on the half-real axis with values in the classical Banach sequence space consisting of real bounded sequences. The main tool used in our investigations is the technique associated with the measures of noncompactness (MNCs) and a fixed point theorem of Darbo type. The applicability of our result is illustrated by a suitable example at the end of the paper.<\/jats:p>","DOI":"10.3390\/sym16010107","type":"journal-article","created":{"date-parts":[[2024,1,16]],"date-time":"2024-01-16T04:03:30Z","timestamp":1705377810000},"page":"107","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Asymptotically Stable Solutions of Infinite Systems of Quadratic Hammerstein Integral Equations"],"prefix":"10.3390","volume":"16","author":[{"given":"J\u00f3zef","family":"Bana\u015b","sequence":"first","affiliation":[{"name":"Department of Nonlinear Analysis, Faculty of Mathematics and Applied Physics, Rzesz\u00f3w University of Technology, Al. Powsta\u0144c\u00f3w Warszawy 8, 35-959 Rzesz\u00f3w, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1661-0028","authenticated-orcid":false,"given":"Justyna","family":"Madej","sequence":"additional","affiliation":[{"name":"Department of Nonlinear Analysis, Faculty of Mathematics and Applied Physics, Rzesz\u00f3w University of Technology, Al. Powsta\u0144c\u00f3w Warszawy 8, 35-959 Rzesz\u00f3w, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Corduneanu, C. (1991). Integral Equations and Applications, Cambridge University Press.","DOI":"10.1017\/CBO9780511569395"},{"key":"ref_2","unstructured":"Pogorzelski, W. (1966). Integral Equations and Their Applications, Pergamon Press, Oxford-New York-Frankfurt, PWN-Polish Scientific Publishers."},{"key":"ref_3","unstructured":"Burton, T.A. 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