On 𝜉^(𝑠)-Quadratic Stochastic Operators on Two-Dimensional Simplex and Their Behavior

Table 1

(a)  

Case	ℙ12	ℙ13	ℙ23
𝐈1	(𝑎,1−𝑎,0)	(𝑎,1−𝑎,0)	(0,0,1)
𝐈2	(0,𝑎,1−𝑎)	(0,𝑎,1−𝑎)	(1,0,0)
𝐈3	(𝑎,0,1−𝑎)	(𝑎,0,1−𝑎)	(0,1,0)
𝐈4	(0,0,1)	(0,0,1)	(𝑎,1−𝑎,0)
𝐈5	(1,0,0)	(1,0,0)	(0,𝑎,1−𝑎)
𝐈6	(0,1,0)	(0,1,0)	(𝑎,0,1−𝑎)

(b)  

Case	ℙ11	ℙ22	ℙ33
𝐈𝐈1	(1,0,0)	(0,1,0)	(0,0,1)
𝐈𝐈2	(0,1,0)	(1,0,0)	(0,0,1)
𝐈𝐈3	(0,0,1)	(0,1,0)	(1,0,0)
𝐈𝐈4	(1,0,0)	(0,0,1)	(0,1,0)
𝐈𝐈5	(0,0,1)	(1,0,0)	(0,1,0)
𝐈𝐈6	(0,1,0)	(0,0,1)	(1,0,0)