Abstract:Using modified Halpern iterations, by elementary method, we extend and improve results obtained by W.A. Kirk (Proc. Amer. Math. Soc. {29} (1971), 294) and others, which have recently been presented in Chapter 11 of {Handbook of Metric Fixed Point Theory} (2001).
Keywords: lipchitzian mapping, uniformly lipschitzian mapping, $n$-periodic mapping, fixed point
AMS Subject Classification: 47H09, 47H10