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Fixed Points Results in Algebras of Split Quaternion and Octonion

Division of Science and Technology, University of Education, Lahore 54000, Pakistan
Department of Mathematics, Government College University, Lahore 54000, Pakistan
Department of Mathematics, University of Okara, Okara 56300, Pakistan
Department of Mathematics and RINS, Gyeongsang National University, Jinju 52828, Korea
Center for General Education, China Medical University, Taichung 40402, Taiwan
Authors to whom correspondence should be addressed.
Symmetry 2018, 10(9), 405;
Received: 3 August 2018 / Revised: 11 September 2018 / Accepted: 14 September 2018 / Published: 17 September 2018
(This article belongs to the Special Issue Discrete Mathematics and Symmetry)
PDF [299 KB, uploaded 17 September 2018]


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. View Full-Text
Keywords: fixed point; split-quaternion; quadratic polynomial; split-octonion fixed point; split-quaternion; quadratic polynomial; split-octonion
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Munir, M.; Naseem, A.; Rasool, A.; Saleem, M.S.; Kang, S.M. Fixed Points Results in Algebras of Split Quaternion and Octonion. Symmetry 2018, 10, 405.

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