A New Hybrid Iterative Scheme for Approximating Fixed Points for Contraction Mappings in Banach Spaces

This study proposes a novel hybrid iterative scheme for approximating fixed points of contraction mappings called Picard-P iterative scheme, which is a combination of Picard and P iterative schemes. The efficiency of present iterative scheme is to provide faster convergence in contrast to several well-known iterative schemes. It is efficiently illustrated with the help of a numerical example followed by a graph. Some convergence and stability results for contraction mappings in the context of Banach spaces are established using the proposed scheme. Additionally, to support our claim, MATLAB programme is used to approximate fixed points for contraction mappings.