Approximation of Fixed Point and Solution for φ-Hemicontraction and φ-Strongly Quasi-Accretive Operator without Lipschitz Assumption

Abstract:

      Let X be a real uniformly smooth Banach space and let T:D(T)?X→X be φ-hemicontractive and locally bounded at its fixed point q∈F(T).Under somesuitable assumptions on the iteration parameters {α_n}and{β_n},we have proved thatthe Mann and Ishikawa iteration processes for T converge strongly to the unique fixedpoint q of T.Several related results deal with iterative solutions of nonlinear equationsinvolving φ-strongly quasi-accretive operators.Our results extend and generalize thosecorresponding ones by Xu and Roach, Zhou and Jia and others.