Some results on convergence of Newton's method in Banach spaces are established under the assumption that the derivative of the operators satisfies the radius or center Lipschitz condition with a weak L average.
The convergence problem of the family of Euler-Halley methods is considered under the Lipschitz condition with the L-average, and a united convergence theory with its applications is presented.
Let G be a non-empty closed (resp. bounded closed) boundedly relatively weakly compact subset in a strictly convex Kadec Banach space X. Let denote the space of all non-empty compact convex subsets of X endowed with ...Let G be a non-empty closed (resp. bounded closed) boundedly relatively weakly compact subset in a strictly convex Kadec Banach space X. Let denote the space of all non-empty compact convex subsets of X endowed with the Hausdorff distance. Moreover, let denote the closure of the set . We prove that the set of all , such that the minimization (resp. maximization) problem min(A,G) (resp. max(A,G)) is well posed, contains a dense G δ-subset of , thus extending the recent results due to Blasi, Myjak and Papini and Li.展开更多
The concept of an RS–set in a complex Banach space is introduced and theproblem of best approximation from an RS–set in a complex space is investigated. Results consistingof characterizations, uniqueness and strong ...The concept of an RS–set in a complex Banach space is introduced and theproblem of best approximation from an RS–set in a complex space is investigated. Results consistingof characterizations, uniqueness and strong uniqueness are established.展开更多
文摘Some results on convergence of Newton's method in Banach spaces are established under the assumption that the derivative of the operators satisfies the radius or center Lipschitz condition with a weak L average.
基金This project is supported by the Special Funds for Major State Basic Research Projects(Grant No. G19990328) the National Natural Science Foundation of China(Grant No. 10271025) also supported partly by Zhejiang Provincial Natural Science Foundation o
文摘The convergence problem of the family of Euler-Halley methods is considered under the Lipschitz condition with the L-average, and a united convergence theory with its applications is presented.
基金partly supported by the National Natural Science Foundation of China(Grant No,10271025)
文摘Let G be a non-empty closed (resp. bounded closed) boundedly relatively weakly compact subset in a strictly convex Kadec Banach space X. Let denote the space of all non-empty compact convex subsets of X endowed with the Hausdorff distance. Moreover, let denote the closure of the set . We prove that the set of all , such that the minimization (resp. maximization) problem min(A,G) (resp. max(A,G)) is well posed, contains a dense G δ-subset of , thus extending the recent results due to Blasi, Myjak and Papini and Li.
基金Supported in part by the National Natural Science Foundation of China(Grant No.10271025) 41A29,41A50
文摘The concept of an RS–set in a complex Banach space is introduced and theproblem of best approximation from an RS–set in a complex space is investigated. Results consistingof characterizations, uniqueness and strong uniqueness are established.
