Vol. 5 No 10 - Pi Mu Epsilon

= lim hp(U(xf, y), U(xffy))Ip(V(xl, Y), v(xrrY Y ))xr+ x p(xfy xrrl p(xf, xr9= h(max(b t cy e t f) = h(b t c, e t f).(I+) a 2 b and c 5 d imply max(ay c) 2 max(by dl. Nowyc(max(a, b) ) = max(ca, cb) since "d 2 kl' and "cd > ck" areequivalent for c 2 0.h(n, b) = b are clear.The equations h(a, 0) = a andApplying Theorem 2 to the function h of Remark 2 gives the follow-ing result.Coko.&by:Let X be a metric space with meeic p and let g be themetric on XxX given by g((xr, yr), (xrry yrr)) = max@(xl, xrr), p(yr, yrr)l.Furthermore, let f:(XxX, g) + (XxX, g) with f(x, y) = (U(x, yIy V(xy y))where U,V : XxX -+ X and