{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T01:28:21Z","timestamp":1773883701728,"version":"3.50.1"},"reference-count":30,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2018,8,1]],"date-time":"2018-08-01T00:00:00Z","timestamp":1533081600000},"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>We study a q-analogue of Euler numbers and polynomials naturally arising from the p-adic fermionic integrals on Zp and investigate some properties for these numbers and polynomials. Then we will consider p-adic fermionic integrals on Zp of the two variable q-Bernstein polynomials, recently introduced by Kim, and demonstrate that they can be written in terms of the q-analogues of Euler numbers. Further, from such p-adic integrals we will derive some identities for the q-analogues of Euler numbers.<\/jats:p>","DOI":"10.3390\/sym10080311","type":"journal-article","created":{"date-parts":[[2018,8,1]],"date-time":"2018-08-01T11:22:34Z","timestamp":1533122554000},"page":"311","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["On p-Adic Fermionic Integrals of q-Bernstein Polynomials Associated with q-Euler Numbers and Polynomials \u2020"],"prefix":"10.3390","volume":"10","author":[{"given":"Lee-Chae","family":"Jang","sequence":"first","affiliation":[{"name":"Graduate School of Education, Konkuk University, Seoul 143-701, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Taekyun","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Kwangwoon University, Seoul 139-701, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9599-7015","authenticated-orcid":false,"given":"Dae San","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Sogang University, Seoul 121-742, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dmitry Victorovich","family":"Dolgy","sequence":"additional","affiliation":[{"name":"Kwangwoon Institute for Advanced Studies, Kwangwoon University, Seoul 139-701, Korea"},{"name":"Institute of National Sciences, Far Eastern Federal University, 690950 Vladivostok, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,8,1]]},"reference":[{"key":"ref_1","first-page":"272","article-title":"A new approach to q-Bernoulli numbers and q-Bernoulli polynomials related to q-Bernstein polynomials","volume":"2015","author":"Erdal","year":"2010","journal-title":"Adv. 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