On the Comparison of Ishikawa-Type Iterative Processes for Contraction Mappings in Banach Spaces With Graphs

This is the authors' abstract. We don't add key points for this paper.

It is well-known that there are many results on convergence to a common fixed point of contraction map ping s for iterative processes with graphs. However, there are few results related to comparing the convergence rates of these iterative processes. In this paper, we consider the comparisons with respect to convergence rates of several Ishikawa-type iterative processes to a common fixed point of contraction mappings in Banach spaces with graphs. More specifically, we propose some sufficient conditions to ensure that an iteration process is faster than the other one. Our work improves the results of a recent one related to the comparison of convergence rates of two-step and three-step iteration sequences. Roughly speaking, the assumptions we make are better for parameter ranges than the previous results. An interesting point is that our paper opens up the new idea of building an optimal hypothesis to obtain a comparison of the convergence rates of general iterative processes.