Name
Title | ||
|---|---|---|
Iterative algorithm for common fixed points of infinite family of nonexpansive mappings in banach spaces |
Abstract | ||
|---|---|---|
Let C be a nonempty closed convex subset of a real uniformly smooth Banach space X, {T-k}(k=1)(infinity) : C -> C an infinite family of nonexpansive mappings with the nonempty set of common fixed points boolean AND(infinity)(k=1) Fix(T-k), and f : C -> C a contraction. We introduce an explicit iterative algorithm x(n+1) = alpha(n)f(x(n)) + (1 - alpha(n))L(n)x(n), where L-n = Sigma(n)(k=1)(omega(k)/s(n))T-k, S-n = Sigma(n)(k=1)omega(k), and omega(k) > 0 with Sigma(infinity)(k=1)omega(k) = 1. Under certain appropriate conditions on {alpha(n)}, we prove that {x(n)} converges strongly to a common fixed point x* of {T-k}(k=1)(infinity), which solves the following variational inequality: < x* - f(x*), J(x* - p)> <= 0, p is an element of boolean AND(infinity)(k=1) Fix(T-k), where J is the (normalized) duality mapping of X. This algorithm is brief and needs less computational work, since it does not involve W-mapping. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1155/2012/787419 | JOURNAL OF APPLIED MATHEMATICS |
Keywords | Field | DocType |
null | Discrete mathematics,Mathematical optimization,Mathematical analysis,Iterative method,Banach space,Regular polygon,Fixed point,Mathematics | Journal |
Volume | Issue | ISSN |
2012 | null | 1110-757X |
Citations | PageRank | References |
0 | 0.34 | 4 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Songnian He | 1 | 42 | 8.08 |
| Jun Guo | 2 | 0 | 0.34 |