tailieunhanh - Báo cáo hóa học: " Some results on a general iterative method for k-strictly pseudo-contractive 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: Some results on a general iterative method for k-strictly pseudo-contractive mappings | Jung Fixed Point Theory and Applications 2011 2011 24 http content 2011 1 24 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Some results on a general iterative method for k-strictly pseudo-contractive mappings Jong Soo Jung Correspondence jungjs@mail. Department of Mathematics Dong-A University Busan 604-714 Korea SpringerOpen0 Abstract Let H be a Hilbert space C be a closed convex subset of H such that C C c C and T C H be a k-strictly pseudo-contractive mapping with F T 0 for some 0 k 1. Let F C C be a K-Lipschitzian and h-strongly monotone operator with K 0 and h 0 and f C C be a contraction with the contractive constant a e 0 1 . 2 Let 0 F 2ị 0 Y 2 r. and T 1. Let an and 3n be sequences in 0 1 . It is proved that under appropriate control conditions on an and j0n the sequence xn generated by the iterative scheme xn 1 angf xn bnxn 1 - bn I -anpF PCSxn where S C H is a mapping defined by Sx kx 1 - k Tx and PC is the metric projection of H onto C converges strongly to q e F T which solves the variational inequality uFq - f q q - p 0 for p e F T . MSC 47H09 47H05 47H10 47J25 49M05 Keywords Iterative schemes k-strictly pseudo-contractive mapping Nonexpansive mapping Fixed points Contraction K-Lipschitzian n-strongly monotone operator Variational inequality Hilbert space 1 Introduction Let H be a real Hilbert space and C be a nonempty closed convex subset of H. Recall that a mapping f C C is a contraction on C if there exists a constant a e 0 1 such that fx -f y á a x - y x y e C. A mapping T C H is said to be k-strictly pseudo-contractive if there exists a constant k e 0 1 such that Tx- TyU2 x - y 2 fc I - T x - I - T y 2 x y e C and F T denote the set of fixed points of the mapping T that is F T x e C Tx x . Note that the class of k-strictly pseudo-contractions includes the class of non-expan-sive mappings T on C that is Tx - Ty x - y x y e C as a subclass. That is T is .