Faster Fixed Point Iterative Scheme for Contraction Mappings

Abstract

In this paper, it is our aim to construct and study a new iteration scheme for the
approximation of fixed points of several contraction mappings in the sense of
Berinde. We prove strong convergence result for the suggested scheme under
Lipchitz conditions. In addition, we demonstrate numerical simulations through
tables and graphs displays to show that our suggested innovative scheme converges
faster than many previously introduced iterative schemes for this mapping also in
the sense of Berinde. Furthermore, a stability analysis under perturbation test is
carried out. The results shows that with any given perturbation, the perturbed
sequences also converges to the fixed of the mapping under investigation same as
the unperturbed sequence. Our findings shows the effectiveness of our suggested
scheme and can be used in approximating fixed points of contraction mappings
and its applications in the field of epidemiology, engineering and computer science.