Study the well-pose, Ulam-Hyers and Ostroxski stability of x=f(x) , x∈X , f:X→X is a Reich operator

x = f(x) is the fixed point equation and (X,d) is a complete metric space.
f : X ~> X is a Reich operator if there exists α,β>=0 with α + 2β < 1 such that
d(f(x),f(y))≤αd(x,y)+β[d(x,f(x))+d(y,f(y))], for every x,y∈X