Strong convergence of an iterative algorithm for pseudocontractive mapping in Banach spaces Original Research Article

Let CC be a nonempty closed convex subset of a real uniformly smooth Banach space XX, T:C→CT:C→C a pseudocontractive mapping. Let {αn}{αn}, {βn}{βn} and {γn}{γn} be three real sequences in (0,1)(0,1) satisfying appropriate conditions; then for fixed u∈Cu∈C and arbitrary x0∈Cx0∈C, the sequence {xn}{xn} generated by View the MathML sourcexn=αnu+βnxn−1+γnTxn,n≥1, converges strongly to a fixed point of TT.