Approximate fixed point sequence for a finite family of asymptotically pseudocontractive mappings

作者：Gu Feng^*

来源：Computers & Mathematics with Applications, 2007, 53(12): 1792-1799.

DOI：10.1016/j.camwa.2006.12.017

• approximated fixed point sequence
• uniformly asymptotically regular mapping
• asymptotically pseudocontractive mapping

Let E be a real Banach space and K be a nonempty, closed, convex, and bounded subset of E. Let T-i : K -> K, i = 1, 2, . . . , N, be N uniformly L-Lipschitzian, uniformly asymptotically regular with sequences {epsilon(n)}, and asymptotically pseudocontractive mappings with sequences {k(n)((i))}, where {epsilon(n)} and {k(n)((i))}, i = 1, 2, N, satisfy certain mild conditions. Let a sequence {x(n)} be generated from x(1) epsilon K by
x(n+1) := lambda(n)theta(n)x(1) + [1 - lambda(n) (1 + theta(n) (1 + mu(n)))]x(n) + lambda T-n(n)n x(n) + lambda(n)theta(n)mu(n)u(n),
for all integers n >= 1, where T-n = T-n(mod N), {u(n)} be a sequence in K, and {lambda(n)}, {theta n} and {mu(n)} are three real sequences in, [0, 1] satisfying appropriate conditions; then parallel to x(n) - T(1)x(n) parallel to -> 0 as n -> infinity for each 1 epsilon {1, 2, . . .,N}.

• 出版日期2007-6
• 单位杭州师范大学