Equivalence of Picard‐type Hybrid Iterative Algorithms for Contractive Mappings

Background and Objective: Fixed point iterative algorithms are designed to be applied in solving equations arising in physical formulation but there is no systematic study of numerical aspects of these iterative algorithms. The Picard, Mann, Ishikawa, Noor and multi step iterative algorithms are the commonly used iterative algorithms in proving fixed point convergence and stability results of different classes of mappings. The objectives of this study therefore were: (1) To develop a Picard‐type hybrid iterative algorithm called Picard‐Mann, Picard‐Ishikawa, Picard‐Noor and Picard‐multistep iterative algorithms, (2) Prove equivalence of convergence theorems using these algorithms for a general class of mappings in a normed linear space and (3) Provide numerical examples to justify the applicability of the algorithms. Materials and Methods: Analytical method was used to prove the main theorem, while numerical method was to demonstrate the application of the equivalence results. Results: Strong convergence, equivalence and numerical results constitute the main results of this study. Conclusion: The results obtained from this study showed that the Picard‐type hybrid iterative algorithms have good potentials for further applications, especially in terms of rate of convergence