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Note on “stability and data dependence results for jungck-type iteration scheme”
Article ID: 2919
Vol 2, Issue 1, 2024
DOI: https://doi.org/10.54517/mss2919
Vol 2, Issue 1, 2024
Received: 29 May 2024; Accepted: 20 June 2024; Available online: 27 June 2024; Issue release: 30 June 2024
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Abstract
This note reviews the iterative methods introduced in “Stability and Data Dependence Results for Jungck-Type Iteration Scheme”. It has been observed that these methods are not entirely new to a significant extent, as they bear resemblance to previously established approaches. Additionally, the primary iterative method proposed in the paper lacks efficiency, particularly when compared to more advanced or well-known methods. As a result, while the methods may offer some value, they do not represent a significant breakthrough in iterative techniques.
Keywords
algorithms; iteration methods; convergence order
References
Kang SM, Rafiq A, Kwun YC. A new second-order iteration method for solving nonlinear equations. Abstract and Applied Analysis. 2013; (SI07): 1–4
Rafiq A, Tanveer M, Kang SM, et al. The modified Jungck Mann and modified Jungck Ishikawa iteration schemes for Zamfirescu operators. International Journal of Pure and Applied Mathematics. 2015; 2(102): 357–382.
Singh SL, Bhatnagar C, Mishra SN. Stability of Jungck-type itera-tive procedures. Int. J. Math. Math. Sci. 2005; 19: 3035–3043.
Kirk WA. On successive approximations for nonexpansive mappings in Banach spaces. Glasgow Mathematical Journal. 1971; 12: 6–9.
Mann WR. Mean value methods in iteration. Proc. Amer. Math. Soc. 1953; 4: 506–610.
Sharma P, Argyros IK, Behl R, Kanwar V. Stability and data dependence results for Jungck-Type iteration scheme. Contemporary Mathematics. 2024; 5(1): 743–760.
Jungck G. Commuting mappings and fixed points. The American Mathematical Monthly. 1976; 83(4): 261–263.
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Copyright (c) 2024 Arif Rafiq
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