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I have this problem that I simply cannot nail down. Please help.

xi - fixed point of g, g is twice continuously differentiable in a vecinity of xi.

z(n+1) = g(g(z(n))) - [g(g(z(n))) - g(z(n))]^2 / [g(g(z(n))) - 2*g(z(n)) + z(n)]

Using taylor series expansion of g(z(n)) and g(g(z(n))) in a vecinity of xi I have to prove that xi is z's limit and that the convergence is quadratic.

Thank you for your help!

Radu