Strong Convergence Of Two Fixed Point Algorithms For Generalized Nonexpansive Mappings

This paper mainly studies the common element method for the solution of fixed point and equilibrium problem of Asymptotically Nonexpansive mapping in Real 4)7)(70)space.By using Halpern-type iterative algorithm,we construct a modified iterative sequence.Under suitable weak conditions,we prove the strong convergence of the sequence.The results here have wider adaptability,including some recent results as special cases.At the same time,a new hybrid iterative algorithm is proposed to solve the split common fixed point problem of strict pseudo-compression mapping,and the strong convergence of the iterative sequence is proved.Therefore,it improves some important conclusions of relevant literature.The structure of this paper is that: we introduce some related research backgrounds,some definitions and related lemmas in the first chapter;In the second chapter,A common iterative halpern-like method is given for asymptotically nonexpansive mapping of fixed point and equilibrium solutions in Hilbert spaces;In the third chapter,strong convergence theorem is proved for iterative solutions to the split common fixed point problem of strictly pseudo-contractive mappings.