Fixed Points of Quadratic Operators Defined on a Three-Dimensional Simplex of Idempotent Measures

In this paper, the set of all fixed points of each quadratic operator, which maps the three-dimensional simplex of idempotent measures to itself, is considered. The $$i$$ th element of $$I_{n}$$ is determined by the aid of all elements of $$i$$ th matrix of the cubic matrix $$P$$ . All quadratic operators, which map the $$(n-1)$$ -dimensional simplex of idempotent measures to itself, is classified. The set of all fixed points of each quadratic operator, which maps the three-dimensional simplex of idempotent measures to itself, is described.

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