STRONG CONVERGENCE OF A MODIFIED ISHIKAWA ITERATIVE ALGORITHM FOR LIPSCHITZ PSEUDOCONTRACTIVE MAPPINGS
M.O. Osilike, Felicia Obiageli Isiogugu, Felix U Attah · Journal of applied mathematics & informatics · 2013
Let H be a real Hilbert space and let T : H ${\rightarrow}$ H be a Lipschitz pseudocontractive mapping. We introduce a modified Ishikawa iterative algorithm and prove that if $F(T)=\{x{\in}H:Tx=x\}{ eq}{\emptyset}$ , then our proposed iterative algorithm converges strongly to a fixed point of T. No compactness assumption is imposed on T and no further requirement is imposed on F(T).