Introduction
Takahashi [ 1 ] introduced a notion of convex metric spaces and studied the fixed point theory for nonexpansive mappings in such setting. For further investigations in this setting the reader may consult [24] and references therein. For the convex metric spaces Kirk [S] and Goebel and Kirk [6] use the term “hyperbolic type space.” They studied the iteration processes for nonexpansive mappings in the abstract framework and generalize and unify some known results in [7, S]. In this paper, we shall deal with Ishikawa’s iteration scheme to construct fixed points of quasi-contractive, generalized quasi-contractive, and quasinonexpansive mappings in convex metric spaces. Our results generalize and unify the corresponding results in 10-17