Xp. Ding et Hl. Zhang, Iterative process to phi-hemicontractive operator and phi-strongly accretive operator equations, APP MATH ME, 21(11), 2000, pp. 1256-1263
Let E be an arbitrary real Banach space and K be a nonempty closed convex s
ubsets of E. let T: K --> K be a uniformly continuous phi -hemicontractive
operator with bounded range and {a(n)}, {b(n)}, {c(n)}, {a(n)'}, {b(n)'}, {
c(n)'} be sequences in [0,1] satisfying: i) a(n) + b(n) + c(n) = a(n)' + b(
n)' + c(n)' = 1, For All n greater than or equal to 0; ii) limb(n) = limb(n
) = limc(n) = 0; iii) (n=0)Sigma (infinity) b(n) = infinity; iv) c(n) = o(b
(n)). For any given x(0), u(0), v(0) is an element of K, define the Ishikaw
a type iterative sequence {x(n)} as follows :
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where {u(n)} and {v(n)} are bounded sequences in K. Then {x(n)} converges s
trongly to the unique fixed point of T. Related result deals with the conve
rgence of Ishikawa type iterative sequence to the solution of phi -strongly
accretive operator equation.