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Keywords:
lipchitzian mapping; uniformly lipschitzian mapping; $n$-periodic mapping; fixed point
lipchitzian mapping; uniformly lipschitzian mapping; $n$-periodic mapping; fixed point
Summary:
Using modified Halpern iterations, by elementary method, we extend and improve results obtained by W.A. Kirk (Proc. Amer. Math. Soc. {\bf 29} (1971), 294) and others, which have recently been presented in Chapter 11 of {\it Handbook of Metric Fixed Point Theory\/} (2001).
References:
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[6] Kim T.H., Kirk W.A.: Fixed point theorems for lipschitzian mappings in Banach spaces. Nonlinear Anal. 26 (1996), 1905-1911. MR 1386122 | Zbl 0856.47031
[7] Kirk W.A.: A fixed point theorem for mappings with a nonexpansive iterate. Proc. Amer. Math. Soc. 29 (1971), 294-298. MR 0284887 | Zbl 0213.41303
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