值域有界的一类非线性算子不动点的带误差迭代逼近

Iterative Approximation with Errors of Fixed Point for a Class of Nonlinear Operation with a Bounder Range

Deptartment of Basic Science, Ordnance Engineering College, Shijianzhuang 050003, P R China

摘要: 设X为一致光滑实Banach空间。T:X→X为连续强增生算子。∀f∈X。定义算子S:X_x→X为S_x=f-T_x+x,∀x∈X。设{α_n}_n^∞=0与{β_n}_n^∞=0为两个给定的实数列在(0,1)中且满足条件:(ⅰ)α_n→0,β_n→0(n→∞)。。假设{u_n}_n^∞=0和{v_n}_n^∞=0为X_x中两个序列且满足‖u_n‖=o(α_n),‖v_n‖→0(n→∞)。∀x₀∈X,迭代序列{x_sn}定义为:若有界,则{x_n}强收敛于S的唯一不动点。
- 一致光滑实Banach空间 /
- 带误差的Ishikawa迭代 /
- 强增生算子
Abstract: Let X be a uniformly smooth real Banach space. Let T:X→X be a continuous and strongly accretive operator. For a given ∀f∈X,define S:X_x→X,for all ∀x∈X,Let {α_n}_n^∞=0 be two real sequences in(0,1) satisfying:(ⅰ)α_n→0,β_n→0(n→∞);.Assume that {u_n}_n^∞=0 and {v_n}_n^∞=0 are two sequences in X satisfying ‖un‖= o (A_n) and ‖v_n‖→0 as n→∞].For arbitrary x₀∈X, the iteration sequence {x_n} is defined by Moreover, suppose that {S_nx_n} and {Sy_n} are bounded, then {x_n} converges strongly to the unique fixed point of S.
- uniformly smooth real Banach spaces /
- I shikawa iteration with errors /
- strongly accretive operator

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