Fixed Points Results in Algebras of Split Quaternion and Octonion

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...

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Bibliographic Details
Published in:Symmetry (Basel) 2018-09, Vol.10 (9), p.405
Main Authors: Munir, Mobeen, Naseem, Asim, Rasool, Akhtar, Saleem, Muhammad Shoaib, Kang, Shin Min
Format: Article
Language:English
Subjects:
Control theory
fixed point
Fixed points (mathematics)
Game theory
Geometry
Gravity
Linear algebra
Mathematical analysis
Mathematics
Multiplication & division
Polynomials
quadratic polynomial
Quaternions
Signal processing
Spacetime
split-octonion
split-quaternion
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Summary: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.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym10090405