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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Akanksha Saxena & Jai Prakash Jaiswal & Kamal Raj Pardasani & Ioannis K. Argyros, 2023. "Extending the Domain with Application of Four-Step Nonlinear Scheme with Average Lipschitz Conditions," Mathematics, MDPI, vol. 11(8), pages 1-23, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1774-:d:1118498
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