Abstract
In this paper we proves the convergence of a convex sequence xn = λxn-1 + (1 - λ)ƒ(xn-1), λ Є (0,1), to a fixed point of the nonexpansive completely continuous operator in the normed ƒ λ -orbitally complete spaces with λ-uniformly convex sphere. Further we shall prove some fixed point theorems of the star-shaped sets.
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