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Advances in Fixed Point Theory ISSN 1927-6303 (Print)

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Adv. Fixed Point Theory 14 (2024), Article ID 46

A new fixed point approximation method for solving third-order BVPs based on Green's function

R. E. Orim, M. O. Udo, A. Maharaj, O. K. Narain

PDF (142.4 KB) https://doi.org/10.28919/afpt/8752

Abstract

This study presents an interesting method based on Picard-Ishikwa fixed point iterative method to solve nonlinear third-order boundary value problems. We develop a sequence called Picrad-Ishikawa Green’s iterative method and show that the sequence converges strongly to the fixed point of an integral operator. Our result improve many existing results in this direction.

Published
26 August 2024
Volume
14 (2024)
License
CC BY 3.0

Copyright © 2024 R. E. Orim, M. O. Udo, A. Maharaj, O. K. Narain. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Cite this article

R. E. Orim, M. O. Udo, A. Maharaj, O. K. Narain, A new fixed point approximation method for solving third-order BVPs based on Green's function, Adv. Fixed Point Theory 14 (2024), 46. https://doi.org/10.28919/afpt/8752

BibTeX
@article{Orim2024,
  author  = {Orim, R. E. and Udo, M. O. and Maharaj, A. and Narain, O. K.},
  title   = {A new fixed point approximation method for solving third-order BVPs based on Green's function},
  journal = {Adv. Fixed Point Theory},
  volume  = {14},
  year    = {2024},
  pages   = {46},
  doi     = {10.28919/afpt/8752}
}