Strong convergence to common fixed points using Ishikawa and hybrid methods for mean-demiclosed mappings in Hilbert spaces
In this paper, we establish a strong convergence theorem that approximates a common fixed point of two nonlinear mappings by comprehensively using an Ishikawa iterative method, a hybrid method, and a mean-valued iterative method. The shrinking projection method is also developed. The nonlinear mappings are a general type that includes nonexpansive mappings and other classes of well-known mappings. The two mappings are not assumed to be continuous or commutative. The main theorems in this paper generate a variety of strong convergence theorems including a type of “three-step iterative method”. An application to the variational inequality problem is also given.
Keyword : Ishikawa iteration, hybrid method, shrinking projection method, mean-valued iteration, mean-demiclosed mapping, common fixed point
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