... Point Theory and ApplicationsVolume 2007, Article ID 20962, 12 pagesdoi:10.1155/2007/20962 Research Article Fixed Points of Weakly Contractive Maps and Boundedness of OrbitsJie-Hua Mai and Xin-He ... continuous, and infx∈Xd(x,f (x))= infn∈Nd(x1n,x2n) = infn∈N1/n = 0. Let c5= a7≥ 0 be a real number, and letother coefficients ai, cj,andbkbe all 0, then both (A.1 )and( A.3)hold.Forthegiven(X,d )and ... (A.1 )and( A.3)hold.Forthegiven(X,d )and f : X→ X, since d( f (x), f (y)) ≤ 1, and c5d( f (x), f2(x)) = a7d( f (x), f2(x)) =1, both (A.2 )and( A.4) hold, too. However, it is clear that f has no fixed points, and eachof...