Firstly

the result of theorem 5.10 in reference ［1］ is extended to a more general form of mapping

namely: sup(y∈E)≤‖Tx－Ty‖≤sup(y∈E)(a‖x－y‖+b‖x－Tx‖+c‖x－Ty‖)，x∈K，a

b

c≥0，a+b+c≤1

and it is proved that there are fixed points for this kind of mapping which is from bounded closed convex subset K with normal structure of a reflexive Banach space into itself. Moreover

in convex b-metric space

it is proved that there is a unique fixed point for the mean non-expansive mapping under certain conditions by utilizing the sequence which is generated by Mann iteration.