Fixed Points of Some Classes of Nonexpansive Mappings
Mathematica Moravica, Tome 8 (2004) no. 1.

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In this paper we proves the convergence of a convex sequence $x_n = \lambda x_{n−1} + (1 −\lambda )f(x_{n−1})$, $\lambda \in (0, 1)$, to a fixed point of the nonexpansive completely continuous operator in the normed $f_{\lambda}$-orbitally complete spaces with $\lambda$-uniformly convex sphere. Further we shall prove some fixed point theorems of the star-shaped sets.
Mots-clés : Normed $f_{\lambda}$-orbitally complete spaces with $\lambda$-uniformly convex sphere, Nonexpansive operator, $\lambda$-orbit, Fixed point, Extremal point, Star-shaped sets 
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Branislav Mijajlović. Fixed Points of Some Classes of Nonexpansive Mappings. Mathematica Moravica, Tome 8 (2004) no. 1. https://geodesic-test.mathdoc.fr/item/MM3_2004_8_1_a4/