tailieunhanh - Báo cáo hóa học: " Research Article Iteration Scheme with Perturbed Mapping for Common Fixed Points of a Finite Family of Nonexpansive Mappings"

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 Iteration Scheme with Perturbed Mapping for Common Fixed Points of a Finite Family of Nonexpansive Mappings | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2007 Article ID 29091 10 pages doi 2007 29091 Research Article Iteration Scheme with Perturbed Mapping for Common Fixed Points of a Finite Family of Nonexpansive Mappings Yeong-Cheng Liou Yonghong Yao and Rudong Chen Received 17 December 2006 Revised 6 February 2007 Accepted 6 February 2007 Recommended by Helene Frankowska We propose an iteration scheme with perturbed mapping for approximation of common fixed points of a finite family of nonexpansive mappings Ti N 1. We show that the proposed iteration scheme converges to the common fixed point x e Pl 1Fix Ti which solves some variational inequality. Copyright 2007 Yeong-Cheng Liou et al. 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 and preliminaries Let H be a real Hilbert space with inner product and norm II II respectively. A mapping T with domain D T and range R T in H is called nonexpansive if Tx - Ty x-yll Vx y e D T . Let Ti N 1 be a finite family of nonexpansive self-maps of H. Denote the common fixed points set of Ti N 1 by Pl Fix Ti . Let F H H be a mapping such that for some constants k n 0 F is k-Lipschitzian and n-strongly monotone. Let an c 0 1 Anin 1 c 0 1 and take a fixed number p e 0 2n k2 . The iterative schemes concerning nonlinear operators have been studied extensively by many authors you may refer to 1-12 . Especially in 13 Zeng and Yao introduced the following implicit iteration process with perturbed mapping F. For an arbitrary initial point x0 e H the sequence xn 1 is generated as follows xn anxn-1 1 an Tnxn npF Tnxn l n 1 1 2 where Tn TnmodN. 2 Fixed Point Theory and Applications Using this iteration process they proved the following weak and strong convergence theorems for nonexpansive mappings in Hilbert spaces. Theorem