On the Contraharmonic-mean Newton’s method(CHN)
Ioannis K. Argyrosiargyros@cameron.eduDepartment of Mathematical SciencesLawton, OK 73505, U.S.ACameron UniversityView full profile → , *Manoj K. SinghCorresponding authormanoj07777@gmail.comCollege of TechnologyMeerut 250110, Uttar PradeshSardar Vallabhbhai Patel University of Agriculture and TechnologyIndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 05 Jun 2021
- Accepted:
- 05 Nov 2021
- Published Online:
- 01 Mar 2023
- Article type:
- A
- Language:
- EN
- Article no.:
- JIM-1448
- Pages:
- 231–243
Abstract
Keywords
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References
[1] S. Amat; S. Busquier; S.Plaza: Review of some iterative root-finding methods from a dynamical point of view. Scientia 10, (3) 35(2004).
[2] I. K. Argyros: Convergence and applications of Newton-type iterations. Springer, Berlin. (2008).
[3] I. K. Argyros: Computational Theory of Iterative Methods, Series: Studies in Computational Mathematics. Elsevier Publ. Comp. New York15, (2007).
[4] I. K. Argyros; A. A. Magrenan: Iterative Methods and Their Dynamics with Applications: A Contemporary Study. C R C Press, Taylor and Francis, Boca Raton, Florida 2017.
[5] M. Bezziou; Z. Dahmani; A. Ndiaye: Langevin differential equation of fractional order in non compactness Banach space. Journal of Interdisciplinary Mathematics 23(4), 857-876(2020) DOI: 10.1080/09720502.2020.1730515.
[6] J. Chen; I. K. Argyros; R. P. Agarwal: Majorizing functions and two-point newton-type methods. J. Comput. Appl. Math. 234(5), 1473-1484 (2010).
[7] P. Jarratt: Some fourth order multipoint iterative methods for solving equations. Math. Comp. 20, 434–437 (1966).
[8] F. N. A. Latiff; W. A. M. Othman; N. Kumaresan: Controlling the initial condition of coupled synchronization of chaotic fractional Newton-Leipnik system for its stability with minimal order. Journal of Interdisciplinary Mathematics 24(4), 931-945 (2020) DOI: 10.1080/09720502.2020.1856342.
[9] K. Madhu: Semilocal Convergence Of Sixth Order Method By Using Recurrence Relations In Banach Spaces. Appl. Math. E-Notes 18, 197-208 (2018).
[10] L.V. Kantorovich; G.P. Akilov: Funtional Analysis. Pergamon Press, Oxford. (1982).
[11] L. B. Rall: Computational Solution of Nonlinear Operator Equations. Robert E. Krieger, New York 1979.
[12] M. K. Singh: A Six-order variant of Newton’s method for solving non linear equations. Computational methods in Science Technology 15(2), 185-193(2009).
[13] M. K. Singh; A. K. Singh: Variant of Newton’s Method Using Simpson’s 3/8th Rule. Int. J. Appl. Comput. 6, (20)(2020).
[14] M. K. Singh; A. K. Singh: The Optimal Order Newton’s Like Methods with Dynamics. Mathematics, 9 527, 2021, https://doi.org/10.3390/math9050527.
[15] A.M. Ostrowski: Solutions of Equations and Systems of Equations. Academic Press, New York, London. (1966).
[16] P. K. Parida; D. K. Gupta: Recurrence relations for a newton-like method in banach spaces. J. Comput. Appl. Math. 206, 873–887(2007).
[17] M. A. H. Veron; E. Martinez: On the semilocal convergence of a three steps newton-type iterative process under mild convergence conditions. Numer. Algorithms 70(2), 377–392 (2015).
[18] K. Wang; J. Kou; C. Gu: Semilocal convergence of a sixth-order jarrat method in Banach spaces. Numer. Algorithms 57, 441–456 (2011).
[19] S. Weerakoon; T.G.I. Fernando: A variant of Newton’s method with accelerated third-order convergence. Appl. Math. Lett. 13(8), 87-93(2000).
[20] Q. Wu; Y. Zhao: Third-order convergence theorem by using majorizing functions for a modified Newton’s method in Banach spaces. Appl. Math. Comput. 175, 1515–1524 (2006).
