{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:57:36Z","timestamp":1760151456530,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,3,21]],"date-time":"2022-03-21T00:00:00Z","timestamp":1647820800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We show how to apply the well-known fixed-point approach in the study of the existence, uniqueness, and stability of solutions to some particular types of functional equations. Moreover, we also obtain the Ulam stability result for them. The functional equations that we consider can be used to explain various experiments in mathematical psychology and arise in a natural way in the stochastic approach to the processes of perception, learning, reasoning, and cognition.<\/jats:p>","DOI":"10.3390\/axioms11030143","type":"journal-article","created":{"date-parts":[[2022,3,21]],"date-time":"2022-03-21T13:24:59Z","timestamp":1647869099000},"page":"143","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["On Solutions and Stability of Stochastic Functional Equations Emerging in Psychological Theory of Learning"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5445-9728","authenticated-orcid":false,"given":"Ali","family":"Turab","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Rangsit 12120, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6529-4885","authenticated-orcid":false,"given":"Janusz","family":"Brzd\u0119k","sequence":"additional","affiliation":[{"name":"Faculty of Applied Mathematics, AGH University of Science and Technology, Mickiewicza 30, 30-059 Krak\u00f3w, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5248-2329","authenticated-orcid":false,"given":"Wajahat","family":"Ali","sequence":"additional","affiliation":[{"name":"School of Science, Nanjing University of Science and Technology, Nanjing 210094, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1037\/h0060989","article-title":"Analysis of a verbal conditioning situation in terms of statistical learning theory","volume":"47","author":"Estes","year":"1954","journal-title":"J. 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