Convergence theorems for strictly hemi-contractive maps

It is proved that each of two well-known fixed point iteration methods (the Mann and the Ishikawa iteration methods) converges strongly to the fixed point of strictly hemi-contractive map in real Banach spaces with property (U, λ, m+1,m), λ is an element of R, m is an element of IN. The class of strictly hemi-contractive maps includes all strictly pseudo-contractive maps with nonempty fixed point sets; and Banach spaces with property (U, λ, m+1, m), λ is an element of R, m is an element of IN include the Lp (or lp) spaces, p≥2. Our theorems generalize important known results. (author). 22 refs