tailieunhanh - Báo cáo hóa học: " Fixed point theorems for some new nonlinear mappings in Hilbert spaces"

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: Fixed point theorems for some new nonlinear mappings in Hilbert spaces | Lin et al. Fixed Point Theory and Applications 2011 2011 51 http content 2011 1 51 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Fixed point theorems for some new nonlinear mappings in Hilbert spaces Lai-Jiu Lin 1 Chih-Sheng Chuang1 and Zenn-Tsun Yu2 Correspondence maljlin@. department of Mathematics National Changhua University of Education Changhua 50058 Taiwan Full list of author information is available at the end of the article Springer Abstract In this paper we introduced two new classes of nonlinear mappings in Hilbert spaces. These two classes of nonlinear mappings contain some important classes of nonlinear mappings like nonexpansive mappings and nonspreading mappings. We prove fixed point theorems ergodic theorems demiclosed principles and Ray s type theorem for these nonlinear mappings. Next we prove weak convergence theorems for Moudafi s iteration process for these nonlinear mappings. Finally we give some important examples for these new nonlinear mappings. Keywords nonspreading mapping fixed point demiclosed principle ergodic theorem nonexpansive mapping 1 Introduction Let H be a real Hilbert space and let C be a nonempty closed convex subset of H. Then a mapping T C C is said to be nonexpansive if Tx - Ty x - y for all x y e C. The set of fixed points of T is denoted by F T . The class of nonexpansive mappings is important and there are many well-known results in the literatures. From literatures we observe the following fixed point theorems for nonexpansive mappings in Hilbert spaces. In 1965 Browder 1 gave the following demiclosed principle for nonexpansive mappings in Hilbert spaces. Theorem . 1 Let C be a nonempty closed convex subset of a real Hilbert space H. Let T be a nonexpansive mapping of C into itself and let xn be a sequence in C. If xn - w and Ji xn Txn II 0 then Tw w. In 1971 Pazy 2 gave the following fixed point theorems for nonexpansive .