{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:03:05Z","timestamp":1760241785786,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2018,9,17]],"date-time":"2018-09-17T00:00:00Z","timestamp":1537142400000},"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>Fixed points of functions have applications in game theory, mathematics, physics, economics and computer science. The purpose of this article is to compute fixed points of a general quadratic polynomial in finite algebras of split quaternion and octonion over prime fields     Z p. Some characterizations of fixed points in terms of the coefficients of these polynomials are also given. Particularly, cardinalities of these fixed points have been determined depending upon the characteristics of the underlying field.<\/jats:p>","DOI":"10.3390\/sym10090405","type":"journal-article","created":{"date-parts":[[2018,9,17]],"date-time":"2018-09-17T10:42:20Z","timestamp":1537180940000},"page":"405","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Fixed Points Results in Algebras of Split Quaternion and Octonion"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6719-7376","authenticated-orcid":false,"given":"Mobeen","family":"Munir","sequence":"first","affiliation":[{"name":"Division of Science and Technology, University of Education, Lahore 54000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Asim","family":"Naseem","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government College University, Lahore 54000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Akhtar","family":"Rasool","sequence":"additional","affiliation":[{"name":"Division of Science and Technology, University of Education, Lahore 54000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muhammad Shoaib","family":"Saleem","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Okara, Okara 56300, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shin Min","family":"Kang","sequence":"additional","affiliation":[{"name":"Department of Mathematics and RINS, Gyeongsang National University, Jinju 52828, Korea"},{"name":"Center for General Education, China Medical University, Taichung 40402, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,9,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5905","DOI":"10.1142\/S0217751X06031661","article-title":"Spin gauge theory of gravity in clifford space: A realization of kaluza-klein theory in four-dimensional spacetime","volume":"21","author":"Pavsic","year":"2006","journal-title":"Int. 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