The Construction and Convergence of Ishikawa Iteration for Quasi-Nonexpansive Operator Sequence

A study is made on the fixed points of the quasi-nonexpansive operator sequence with a mapping from the bounded closed convex subset of a uniformly convex Banach space into the closed convex subset in the same space. The sufficient conditions for the quasi-nonexpansive operator sequence to have a common fixed point are obtained, and the corresponding Ishikawa iterative sequence converging on the common fixed point is constructed. The results obtained in this paper are the extension of the conclusions in the recent publication of the author.