In this paper

the most famous result by Wkirk is that the nonexpansive mapping has the fixed point property in a Banach space with normal structure reflexive is extended to a more general form of mapping

namely:‖T(x)－T(y)‖≤a1(t)(d(x

y))‖x－y‖+a2(t)(d(x

y))‖x－T(x)‖+a3(t)(d(x

y))‖x－T(y)‖

where ai(t):(0

+∞)→(0

1) monotone decreases

a reflexive Banach space X with normal structure has the fixed point property for the mapping mentioned above