ON THE COMPARISON OF ISHIKAWA-TYPE ITERATIVE PROCESSES FOR CONTRACTION MAPPINGS IN BANACH SPACES WITH GRAPHS

Tóm tắt

Numerous studies have examined the convergence of iterative processes with graphs to a common fixed point of contraction mappings. However, research comparing the convergence rates of these processes remains limited. This paper addresses this gap by analyzing the convergence rates of several Ishikawa-type iterative processes to a common fixed point of contraction mappings in Banach spaces with graphs. We propose sufficient conditions to determine the relative speed of convergence between iteration processes. Our work extends recent findings on the comparison of convergence rates between two-step and three-step iteration sequences, offering improved parameter range assumptions. Notably, this study introduces a novel approach to formulating optimal hypotheses for comparing convergence rates of general iterative processes