Iterative approximation of common fixed points of generalized nonexpansive maps in convex metric spaces

Abstract

We define SP-iteration procedure associated with three self maps T1; T2; T3 definedon a nonempty convex subset of a convex metric space X and prove -convergence ofthis iteration procedure to a common fixed point of T1; T2; T3 under the hypotheses thateach Ti is either an -nonexpansive map or a Suzuki nonexpansive map in the settingof uniformly convex metric spaces. Also, we prove the strong convergence of this iterationprocedure to a common fixed point of T1; T2; T3 under certain additional hypothesesnamely either semicompact or condition (D).