In order to study the fixed point property in Banach space

J. Garcia-Falset introduces a geometric constant R（a

X） and proves that if ＂R（a

X） 〈 1 ＋a（0 〈a 〈 1）＂sets up in a Banach space X

then X has the fixed point property for non-expansive mapping. On the base of R（ a

X）

a new geometric constant R1 （ a

X） is in- troduced in Banach space. It is proved that the Banach space X has the weak fixed point property for non-expansive mapping if ＂R1 （a

X） 〈 1 ＋ a＂ sets up

and the specific value for the constant Rl （a

X） is given in Orlicz se- quence space with the Luxemburg norm.