Jungck-Type Implicit Iterative Algorithms with Numerical Examples

Abstract

We introduce a new Jungck-type implicit iterative scheme and study its strong convergence, stability under weak parametrical restrictions in generalized convex metric spaces as well as data dependency in generalized hyperbolic spaces. We show that newly introduced iterative scheme has better convergence rate as compared to well known Jungck implicit Mann, Jungck implicit Ishikawa and Jungck implicit Noor iterative schemes. It is also shown that Jungck-implicit iterative schemes converge fast as compared to corresponding Jungck-explicit iterative schemes. Validity of our analytic proofs is shown through numerical examples. Our results are improvements and generalizations of some recent results of Khan et al.[18], Chugh et al.[8] and many others in fixed point theory.