A study in the fixed point theory for a new iterative scheme and a class of generalized mappings

DOI: https://doi.org/10.37193/CMI.2018.02.07

In this study, we introduce a new iteration scheme and prove the strong convergence result for this iteration method. We also compare the rate of convergence with the iterative scheme and the fixed point iteration scheme known as Picard-S due to Gursoy. Then we prove that this new iteration method is equivalent to convergence of the iteration schemes given in the introduction section of the manuscript. Moreover, we show the result of its data dependency.