On a distinct family of iterative schemes for weak contractions

Abstract

This article introduces a distinct collection of fixed point iteration schemes. For this collection, a strong convergence result is established involving weak contractions. Additionally, a comparison result is obtained to compare the speed of convergence of different iterations in the collection. Furthermore, a result comparing some iterations from the collection with several notable and recent iterative schemes from the literatüre is procured. Finally, these comparisons are elucidated by a non-trivial exemplification, which is represented graphically as well. This family of iterations is conjectured to be the fastest in literature for steps more than three.