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Fixed point theorems for $$n$$-periodic mappings in Banach spaces. (English) Zbl 1123.47038
Summary: Using modified Halpern iterations, by elementary method, we extend and improve results obtained by W. A. Kirk [Proc. Am. Math. Soc. 29, 294–298 (1971; Zbl 0213.41303)].

##### MSC:
 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 47H10 Fixed-point theorems
##### Keywords:
Lipschitzian mapping; uniformly Lipschitzian mapping
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