Four Step F-Stable Iterative Technique for Garcia-Falset Mapping with Improved Convergence and Various Applications

Abstract

In thisothesis, Firstowe presentiainewoform of iterative technique. This new itera tiveostrategy forocontraction mappingooutperforms previousomethods suchoas Picard, Thakur etoal.,iand Asghar Rahimi and many more. We compared these iterative meth ods againstoa new iterative strategy and presented the findingsographically.iThe re search investigatesothe convergence of this new iteration to the fixed point inouniformly convexoBanachospaces using GarciaoFalset operator and worked on itsostability. We also present the working of this iterative technique on to a boundaryivalue problem to support our findings. Moreover, exhibit the applicabilityiof four-stepiiteration pro cess in the delayidifferential equations. Finally, we design a training problem for an implicitineural network that can be considered as an extension of traditional Feed forwardinetwork.