tailieunhanh - Báo cáo hóa học: " Strong convergent result for quasi-nonexpansive mappings in Hilbert spaces"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Strong convergent result for quasi-nonexpansive mappings in Hilbert spaces | Tian and Jin Fixed Point Theory and Applications 2011 2011 88 http content 2011 1 88 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Strong convergent result for quasi-nonexpansive mappings in Hilbert spaces Ming Tian and Xin Jin Correspondence tianming1963@ College of Science Civil Aviation University of China Tianjin 300300 China Springer Abstract In this article we study an iterative method over the class of quasi-nonexpansive mappings which are more general than nonexpansive mappings in Hilbert spaces. Our strong convergent theorems include several corresponding authors results. 2000 MSC 58E35 47H09 65J15. Keywords quasi-nonexpansive mapping Lipschitzian continuous strongly monotone nonlinear operator fixed point viscosity method 1. Introduction Let H be a real Hilbert space with inner product and induced norm - . A mapping T H H is called nonexpansive if Tx - Ty x - y for all x y e H. The set of the fixed points of T is denoted by Fix T x e H Tx x . The viscosity approximation method was first introduced by Moudafi 1 in 2000. Starting with an arbitrary initial x0e H define a sequence xn generated by Xn 1 1 n f Xn 1 1g TXn v n 0 1-1 where f is a contraction with a coefficient a e 0 1 on H . fx - fy a x -y for all x y e H T is nonexpansive and en is a sequence in 0 1 satisfying the following given conditions 11 lim . . E 0 12 E n 0 en . 13 lim. 1 - - 0. It is proved that the sequence xn generated by converges strongly to the unique solution x e C C Fix T of the variational inequality I - f x X - X 0 v X e Fix T . In 2003 Xu 2 proved that the sequence xn defined by the below process where T is also nonexpansive started with an arbitrary initial x0 e H Xn 1 anb I - a A TX v n 0 1-2 2011 Tian and Jin licensee Springer. This is an Open Access article distributed underthe terms of the Creative Commons Attribution License http licenses by which permits .