Malaysian Journal of Mathematical Sciences, May 2017, Vol. 11, No. 2
Extremity of \(b\)-bistochastic Quadratic Stochastic Operators on 2D Simplex
Mukhamedov, F. and Embong, A. F.
Corresponding Email: farrukh.m@uaeu.ac.ae
Received date: 8 June 2016
Accepted date: 29 March 2017
Abstract:
In the present paper, we study the set of \(b\)-bistochastic quadratic stochastic operators. Using the description of such kind of operators, we investigate extreme points of the set of \(b\)-bistochastic quadratic stochastic operators (q.s.o) acting on two dimensional simplex. Further, we introduce weaker conditions of extreme points called quasi-extreme of the set \(b\)-bistochastic quadratic stochastic operators (q.s.o) and study its relations with extreme points of the set \(b\)-bistochastic linear stochastic operators defined on two dimensional simplex.
Keywords: Quadratic stochastic operators (q.s.o), \(b\)-order, bistochastic, doubly stochastic, \(b\)-bistochastic, extreme points
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