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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: REGULARIZATION OF NONLINEAR ILL-POSED EQUATIONS WITH ACCRETIVE OPERATORS | REGULARIZATION OF NONLINEAR ILL-POSED EQUATIONS WITH ACCRETIVE OPERATORS YA. I. ALBER C. E. CHIDUME AND H. ZEGEYE Received 11 October 2004 We study the regularization methods for solving equations with arbitrary accretive operators. We establish the strong convergence of these methods and their stability with respect to perturbations of operators and constraint sets in Banach spaces. Our research is motivated by the fact that the fixed point problems with nonexpansive mappings are namely reduced to such equations. Other important examples of applications are evolution equations and co-variational inequalities in Banach spaces. 1. Introduction Let E be a real normed linear space with dual E . The normalized duality mapping j E 2E is defined by j x x e E x x xH2 x x 1.1 where x Ộ denotes the dual product pairing between vectors x e E and ộ e E . It is well known that if E is strictly convex then j is single valued. We denote the single valued normalized duality mapping by J. A map A D A Q E 2E is called accretive if for all x y e D A there exists J x - y e j x - y such that u - v J x - y 0 Vu e Ax Vv e Ay. 1.2 If A is single valued then 1.2 is replaced by Ax - Ay J x - y 0. 1.3 A is called uniformly accretive if for all x y e D A there exist J x - y e j x - y and a strictly increasing function y R 0 to R y 0 0 such that Ax - Ay J x - y y x - yll . 1.4 Copyright 2005 Hindawi Publishing Corporation Fixed Point Theory and Applications 2005 1 2005 11-33 DOI 10.1155 FPTA.2005.11 12 Nonlinear Ill-posed problems with accretive operators It is called strongly accretive if there exists a constant k 0 such that in 1.4 y t kt2. If E is a Hilbert space accretive operators are also called monotone. An accretive operator A is said to be hemicontinuous at a point x0 e D A if the sequence A x0 tnx converges weakly to Ax0 for any element x such that x0 tnx e D A 0 tn t x0 and tn 0 n TO. An accretive operator A is said to be maximal accretive if it is accretive and the inclusion G A Q
