g is not contractive on : . To show that has a fixed point on , think about the intermediate value theorem.
is not the only possibility, . You should try to link the fixed point and the limit of the sequence : let's assume that has a limit . What can be said about ?c)Choose a closed to the fixed point of g in , analyze the convergence of the sequence . This is where I'm stuck in. My work : I chose . I get . Then . It shouldn't be possible! It's not convergent, it will oscillate infinitely!