Xue, Zhiqun Approximation of fixed points of strongly pseudocontractive mappings in uniformly smooth Banach spaces. (English) Zbl 1124.47050 Int. J. Math. Math. Sci. 2006, No. 4, 46561, 6 p. (2006). The author proves the following result. Let \(E\) be a real uniformly smooth Banach space, \(K\) be a nonempty closed convex subset of \(E\), and the map \(T: K \to K\) be continuous and strongly pseudocontractive. Then the Ishikawa iteration scheme converges to the unique fixed point of \(T\). The author buttresses his result with an example of a strongly pseudocontractive map \(T:=T_{1} + T_{2}\) which is neither Lipschitzian nor has a bounded range. Reviewer: Edward Prempeh (Kumasi) MSC: 47J25 Iterative procedures involving nonlinear operators 47H10 Fixed-point theorems 47H06 Nonlinear accretive operators, dissipative operators, etc. Keywords:real uniformly smooth Banach space; continuous and strongly pseudocontractive mapping; Lipschitz map; bounded range map; Ishikawa iterative scheme; strong convergence; fixed point PDFBibTeX XMLCite \textit{Z. Xue}, Int. J. Math. Math. Sci. 2006, No. 4, 46561, 6 p. (2006; Zbl 1124.47050) Full Text: DOI EuDML References: [1] Bogin, J., On strict pseudo-contractions and a fixed point theorem [2] Zhou, H.; Jia, Y., Approximation of fixed points of strongly pseudocontractive maps without Lipschitz assumption, Proceedings of the American Mathematical Society, 125, 6, 1705-1709 (1997) · Zbl 0871.47045 · doi:10.1090/S0002-9939-97-03850-1 [3] Chidume, C. E.; Osilike, M. O., Ishikawa iteration process for nonlinear Lipschitz strongly accretive mappings, Journal of Mathematical Analysis and Applications, 192, 3, 727-741 (1995) · Zbl 0862.47045 · doi:10.1006/jmaa.1995.1200 [4] Deimling, K., Zeros of accretive operators, Manuscripta Mathematica, 13, 4, 365-374 (1974) · Zbl 0288.47047 · doi:10.1007/BF01171148 [5] Zhou, H.; Jia, Y., Approximation of fixed points of strongly pseudocontractive maps without Lipschitz assumption, Proceedings of the American Mathematical Society, 125, 6, 1705-1709 (1997) · Zbl 0871.47045 · doi:10.1090/S0002-9939-97-03850-1 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.