Strong convergence theorems for uniformly continuous pseudocontractive maps

AbstractLet K be a nonempty closed convex subset of a real Banach space E and let T:K→K be a uniformly continuous pseudocontraction. Fix any u∈K. Let {xn} be defined by the iterative process: x0∈K, xn+1:=μn(αnTxn+(1−αn)xn)+(1−μn)u. Let δ(ϵ) denote the modulus of continuity of T with pseudo-inverse ϕ. If {ϕ(t)t:0<t<1} and {xn} are bounded then, under some mild conditions on the sequences {αn}n and {μn}n, the strong convergence of {xn} to a fixed point of T is proved. In the special case where T is Lipschitz, it is shown that the boundedness assumptions on {ϕ(t)t:0<t