Iterative scheme for nonself generalized asymptotically quasi-nonexpansive mappings

作者：Deng Lei^*; Liu Qifei

来源：Applied Mathematics and Computation, 2008, 205(1): 317-324.

DOI：10.1016/j.amc.2008.08.027

• Iterative scheme
• Uniformly L-Lipschitzian
• Nonself generalized asymptotically quasi-nonexpansive mapping
• Uniformly convex Banach space

Let E be a real uniformly convex Banach space, K a nonempty closed convex subset of E, and T(1); T(2) : K -> E two uniformly L-Lipschitzian, nonself generalized asymptotically quasi-non-expansive mappings with nonnegative real sequences {k(n)((i))}, {delta((i))(n)} (i = 1, 2), respectively satisfying Sigma(infinity)(n-1) (k(n)((i)) - 1) < +infinity. Suppose F = F(T(1)) boolean AND F(T(2)) not equal empty set. If, for any x(i) is an element of K (i = 0, 1, 2, ...,q and q is an element of N is a fixed number ), {x(n}) be a sequence in K defined by
{ y(n) = P(<(alpha)over bar>(n)x(n) + (beta) over barT(2)(PT(2))(n-1)x(n) + (gamma) over bar (n)v(n)), n= 0, 1, 2,...,
x(n+1) = P(alpha(n)x(n) + beta(n)T(1) (PT(1))(n-1) y(n-q) + gamma(n)u(n)), n = q,q + 1, q + 2,....,
where Sigma gamma(n) < infinity and Sigma<(gamma)over bar> < infinity. then {x(n)} converges strongly to a common fixed point of T(1,) T(2) under suitable conditions.

• 出版日期2008-11-1
• 单位西南大学