Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Stability and Convergence Results Based on Fixed Point Theory for a Generalized Viscosity Iterative Scheme | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 314581 19 pages doi 2009 314581 Research Article Stability and Convergence Results Based on Fixed Point Theory for a Generalized Viscosity Iterative Scheme M. De la Sen IIDP. Faculty of Science and Technology University of the Basque Country Campus ofLeioa Bizkaia . Box 644 48080 Bilbao Spain Correspondence should be addressed to M. De la Sen Received 18 February 2009 Accepted 27 April 2009 Recommended by Tomas Dominguez Benavides A generalization of Halpern s iteration is investigated on a compact convex subset of a smooth Banach space. The modified iteration process consists of a combination of a viscosity term an external sequence and a continuous nondecreasing function of a distance of points of an external sequence which is not necessarily related to the solution of Halpern s iteration a contractive mapping and a nonexpansive one. The sum of the real coefficient sequences of four of the above terms is not required to be unity at each sample but it is assumed to converge asymptotically to unity. Halpern s iteration solution is proven to converge strongly to a unique fixed point of the asymptotically nonexpansive mapping. Copyright 2009 M. De la Sen. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction Fixed point theory is a powerful tool for investigating the convergence of the solutions of iterative discrete processes or that of the solutions of differential equations to fixed points in appropriate convex compact subsets of complete metric spaces or Banach spaces in general 1-12 . A key point is that the equations under study are driven by contractive maps or at least by asymptotically nonexpansive maps. By that reason the fixed point formalism is useful in stability
