Convergence theorems for strongly pseudo-contractive and strongly accretive maps

[摘要] Suppose E is an arbitrary real Banach space and K is a nonempty closed convex and bounded subset of E. Suppose T: K --> K is a uniformly continuous strong pseudo-contraction with constant k is an element of (0, 1). Suppose {a(n)}, {b,(n)}, {c(n)}, {a(n)'}, {b(n)'}, and {c(n)'} are sequences in (0, 1) satisfying the following conditions: (i) a(n) + b(n) + c(n) = 1 = a(n)' + b(n)' + c(n)' For All integers n greater than or equal to 0; (ii) lim b(n) = lim b(n)' = lim c(n)' = 0; (iii) Sigma b(n) = infinity; (iv) Sigma c(n) < infinity. For arbitrary x(0), u(0), v(0) is an element of K, define the sequence {x(n)}(n=0)(infinity) iteratively by x(n+1) = a(n)x(n) + b(n)Ty(n) + c(n)u(n); y(n) = a(n)'x(n) + b(n)'Tx(n) + c(n)'v(n), n greater than or equal to 0, where {u(n)}, {v(n)} are arbitrary sequences in K. Then {x(n)} converges strongly to the unique fixed point of T. Related results deal with the iterative solutions of nonlinear equations involving set-valued, strongly accretive operators. (C) 1998 Academic Press.

[发布日期] 1998-12-01

[关键词] strong pseudo-contractions;strong accretive operators;Ishikawa and Mann iteration processes;strict hemicontractions