Approximation methods for common fixed points for a countable family of nonexpansive mappings

作者：Chidume C E; Chidume C O; Nwogbaga A P

来源：Nonlinear Analysis-Theory Methods & Applications, 2009, 71(12): E164-E175.

DOI：10.1016/j.na.2008.10.010

• Demiclosed mappings
• Demicompact operator
• Nonexpansive mappings

Let E = L(p) or l(p) space, 1 < p < infinity. Let K be a closed, convex and nonempty subset of E. Let {T(i)}(i=1)(infinity) be a family of nonexpansive self-mappings of K. For arbitrary fixed delta is an element of (0, 1), define a family of nonexpansive maps {S(i)}(i=1)(infinity) by S(i) := (1 - delta)I + delta T(i) where I is the identity map of K. Let F := boolean AND(infinity)(i=1) F(T(i)) not equal empty set. It is proved that the iterative sequence {x(n)} defined by: x(0) is an element of K, x(n+1) = alpha(n)u + Sigma(i >= 1) sigma(i,tn)S(i)x(n), n >= 0 converges strongly to a common fixed point of the family {T(i)}(i=1)(infinity) where {alpha(n)} and {sigma(i,tn)} are sequences in (0, 1) satisfying appropriate conditions, in each of the following cases: (a) E = l(p), 1 < p < infinity, and (b) E = L(p); 1 < p < infinity and at least one of the maps T(i)'s is demicompact. Our theorems extend the results of [P. Mainge, Approximation methods for common fixed points of nonexpansive mappings in Hilbert space, J. Math. Anal. Appl. 325 (2007) 469-479] from Hilbert spaces to l(p) spaces, 1 < p < infinity.

• 出版日期2009-12