Some sequences supplied by inequalities and their applications
In order to prove the convergence of Ishikawa and Mann iterations, the convergence of one type of sequences is needed. Our purpose, in this note, is to give a new proof of the convergence for one of them. We also give generalizations for the sequences.
S. Ishikawa, Fixed Points by a New Iteration Method, Proc. Amer. Math. Soc. 44 (1974), 147-150, https://doi.org/10.1090/s0002-9939-1974-0336469-5
R. W. Mann, Mean Value Methods in Iteration, Proc. Amer. Math. Soc. 4 (1953), 506-510, https://doi.org/10.1090/s0002-9939-1953-0054846-3
J. A. Park, Mann-Iteration for Strictly Pseudocontractive Maps, J. Korean Math. Soc. 31 (1994), 333-337.
H. Y. Zhou, Stable Iteration Procedures for Strong Pseudocontractions and Nonlinear Equations Involving Accretive Operators without Lipschitz Assumption, J. Math. Anal. Appl. 230 (1999), 1-30.
H. Y. Zhou, J. Yuting, Approximation of Fixed Points of Strongly Pseudocontractive Maps without Lipschtzian Assumption, Proc. Amer. Math. Soc. 125 (1997), 1705-1709, https://doi.org/10.1090/s0002-9939-97-03850-1
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