The purpose of this paper is to consider a new implicit iteration and study its strong convergence, stability, and data dependence. It is proved through numerical examples that newly introduced iteration has better convergence rate than well known implicit Mann iteration as well as implicit Ishikawa iteration and implicit iterations converge faster as compared to corresponding explicit iterations. Applications of implicit iterations to RNN (Recurrent Neural Networks) analysis are also presented.

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We introduce a new Jungck-type implicit iterative scheme and study its strong convergence, stability under weak parametric restrictions in generalized convex metric spaces and data dependency in generalized hyperbolic spaces. We show thatnewintroduced 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 faster than the 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.[21], Chugh et al.[8] and many others in fixed point theory.

The aim of this paper is to prove some strong and Δ-convergence results for modified Khan et. al. iterative procedures using total asymptotically quasi-nonexpansive mappings in Hyperbolic spaces. The results are the generalization and extension of some results of Agarwal et. al.

The aim of this paper is to prove some results on strong and △-convergence of S-iterative scheme for SKC mappings in hyperbolic spaces. The results presented here extend and improve the results of Nanjaras et. al. [15], Karapinar and Tas [16] and Khan and Abbas [17].