A Novel Picard-P Hybrid Iterative Scheme: Convergence Analysis and Applications

Abstract

The trend of incorporating the Picard iteration into already established iterative processes has led to highly efficient convergence results, as observed in cases such as the Picard-Noor hybrid, Picard-S^* hybrid, Picard-S hybrid, Picard-Ishikawa hybrid, Picard-Mann hybrid, and several others. Using this technique, in this paper, we have introduced a new hybrid iterative scheme by merging Picard iterative scheme with P iterative scheme. We used numerical example to show the efficiency new Picard-P hybrid iteration process. By using Picard-P hybrid iterative we proved strong and weak fixed point convergence results for Suzuki Generalized Nonexpansive Mapping (SGNEM). As an application we established the solution of delay differential equations using Picard-P hybrid iteration scheme.