Let E be a real reflexive Banach space with a uniformly Gâteaux differentiable norm. Let K be a nonempty bounded closed convex subset of E, and every nonempty closed convex bounded subset of K has the fixed point property for non-expansive self-mappings. Let a contractive mapping and be a uniformly continuous pseudocontractive mapping with . Let be a sequence satisfying the following conditions: (i) ; (ii) . Define the sequence in K by , , for all . Under some appropriate assumptions, we prove that the sequence converges strongly to a fixed point which is the unique solution of the following variational inequality: , for all .
Youli Yu. "An Iterative Algorithm on Approximating Fixed Points of Pseudocontractive Mappings." J. Appl. Math. 2012 (SI03) 1 - 11, 2012. https://doi.org/10.1155/2012/341953