... thank the referees for valuable suggestions. This research issupported by the Centre of Excellence in Mathematics, the Commission on Higher Education, and the Thailand Research Fund. The first ... satisfies the AKTT-condition. By Lemma 2.5,wecandefinethemappingS : C →C by Sx limn →∞Snx for x ∈ C.Hence,Sx γx 1 − γTx, x ∈ C,sinceTnx → Tx for 16 Fixed Point Theory and Applications for ... itself, and let ξ1,ξ2, be real numbers such that 0 <ξi< 1foralli ∈ .Moreover,letWn and W be the W-mappings 35 generated by S1,S2, ,Sn and ξ1,ξ2, ,ξn and S1,S2, and ξ1,ξ2,...