Extending the Domain with Application of Four-Step Nonlinear Scheme with Average Lipschitz Conditions

Akanksha Saxena, Jai Prakash Jaiswal (), Kamal Raj Pardasani and Ioannis K. Argyros ()
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Akanksha Saxena: Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal 462003, MP, India
Jai Prakash Jaiswal: Department of Mathematics, Guru Ghasidas Vishwavidyalaya (A Central University), Bilaspur 495009, CG, India
Kamal Raj Pardasani: Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal 462003, MP, India
Ioannis K. Argyros: Department of Computing and Mathematical Sciences, Cameron University, Lawton, OK 73505, USA

Mathematics, 2023, vol. 11, issue 8, 1-23

Abstract: A novel local and semi-local convergence theorem for the four-step nonlinear scheme is presented. Earlier studies on local convergence were conducted without particular assumption on Lipschitz constant. In first part, the main local convergence theorems with a weak ϰ -average (assuming it as a positively integrable function and dropping the essential property of ND) are obtained. In comparison to previous research, in another part, we employ majorizing sequences that are more accurate in their precision along with the certain form of ϰ average Lipschitz criteria. A finer local and semi-local convergence criteria, boosting its utility, by relaxing the assumptions is derived. Applications in engineering to a variety of specific cases, such as object motion governed by a system of differential equations, are illustrated.

Keywords: local convergence; nonlinear problem; convergence radius; Banach space; generalized Lipschitz conditions; ? -average (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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