abstract:assume that y is a banach space such that r(y ) ? 2, where r(.) is garc?a-falset’s coefficient. and x is a banach space which can be continuously embedded in y . we prove that x can be renormed to satisfy the weak fixed point property (w-fpp). on the other hand, assume that k is a scattered compact topological space such that k(!) = ? ; and c(k) is the space of all real continuous functions defined on k with the supremum norm. we will show that c(k) can be renormed to satisfy r(c(k)) ? 2. thus, both results together imply that any banach space which can be continuously embedded in c(k) , k as above, can be renormed to satisfy the w-fpp. these results extend a previous one about the w-fpp under renorming for banach spaces which can be continuously embedded in c?(??). furthermore, we consider a metric in the space p of all norms in c(k) which are equivalent to the supremum norm and we show that for almost all norms in p (in the sense of porosity) c(k) satisfies the w-fpp. we solve 2 or 3 longtime open question.