[1] S. Amat, C. Berm´udez, M.A. Hern´andez-Ver´on, and E. Mart´ınez, On an efficient k-step iterative method for nonlinear equations, J. Comput. Appl. Math. 302 (2016), 258–271.
[2] S. Amat, S. Busquier, and S. Plaza, Review of some iterative root-finding methods from a dynamical point of view, Scientia 10 (2004), no. 3, 35.
[3] , Chaotic dynamics of a third-order Newton-type method, J. Math. Anal. Appl. 366 (2010), no. 1, 24–32.
[4] S. Amat, J.A. Ezquerro, and M.A. Hern´andez-Ver´on, On a new family of high-order iterative methods for the matrix pth root, Numer. Linear Alg. Appl. 22 (2015), no. 4, 585–595.
[5] S. Amat, M.A. Hern´andez, and N. Romero, Semilocal convergence of a sixth order iterative method for quadratic equations, Appl. Numer. Math. 62 (2012), no. 7, 833–841.
[6] S. Amat, A.A. Magre˜n´an, and N. Romero, ´ On a two-step relaxed Newton-type method, Appl. Math. Comput. 219 (2013), no. 24, 11341–11347.
[7] I.K. Argyros, R. Behl, and S.S. Motsa, Unifying semilocal and local convergence of Newton’s method on Banach space with a convergence structure, Appl. Numer. Math. 115 (2017), 225–234.
[8] I.K. Argyros, Y.J. Cho, and S. Hilout, On the midpoint method for solving equations, Appl. Math. Comput. 216 (2010), no. 8, 2321–2332.
[9] I.K. Argyros, A. Cordero, A.A. Magre˜n´an, and J.R. Torregrosa, ´ Third-degree anomalies of Traub’s method, J. Comput. Appl. Math. 309 (2017), 511–521.
[10] I.K. Argyros and S. Hilout, Extending the Newton–Kantorovich hypothesis for solving equations, J. Comput. Appl. Math. 234 (2010), no. 10, 2993–3006.
[11] , Weaker convergence conditions for the Secant method, Appl. Math. 59 (2014), no. 3, 265–284.
[12] P. Bakhtiari, A. Cordero, T. Lotfi, K. Mahdiani, and J.R. Torregrosa, Widening basins of attraction of optimal iterative methods, Nonlinear Dyn. 87 (2017), no. 2, 913–938.
[13] R. Behl, S. Amat, A.A. Magre˜n´an, and S.S. Motsa, ´ An efficient optimal family of sixteenth order methods for nonlinear models, J. Comput. Appl. Math. 354 (2019), 271–285.
[14] R. Behl, A. Cordero, S.S. Motsa, and J.R. Torregrosa, Stable high-order iterative methods for solving nonlinear models, Appl. Math. Comput. 303 (2017), 70–88.
[15] N.J. Bini, D.A.and Higham and B. Meini, Algorithms for the matrix pth root, Numer. Algorithms 39 (2005), no. 4, 349–378.
[16] P. Blanchard, Complex analytic dynamics on the Riemann sphere, Bull. Amer. Math. Soc. 11 (1984), no. 1, 85–141.
[17] J. Chen, I.K. Argyros, and R.P. Agarwal, Majorizing functions and two-point Newton-type methods, J. Comput. Appl. Math. 234 (2010), no. 5, 1473–1484.
[18] A. Cordero, F. Soleymani, J.R. Torregrosa, and F.K. Haghani, A family of Kurchatov-type methods and its stability, Appl. Math. Comput. 294 (2017), 264–279.
[19] A. Cordero, F. Soleymani, J.R. Torregrosa, and M.Z. Ullah, Numerically stable improved Chebyshev–Halley type schemes for matrix sign function, J. Comput. Appl. Math. 318 (2017), 189–198.
[20] A. Cordero and J.R. Torregrosa, A sixth-order iterative method for approximating the polar decomposition of an arbitrary matrix, J. Comput. Appl. Math. 318 (2017), 591–598.
[21] J.A. Ezquerro, M.A. Hern´andez, and N. Romero, Newton-type methods of high order and domains of semilocal and global convergence, Appl. Math. Comput. 214 (2009), no. 1, 142–154.
[22] J.A. Ezquerro, M.A. Hern´andez, and M.A. Salanova, Recurrence relations for the midpoint method, Tamkang J. Math. 31 (2000), no. 1, 33–42.
[23] P. Fatou, Sur les ´equations fonctionnelles, Bull. Soc. Math. France 47 (1919), no. 48, 1920.
[24] C.-H. Guo, On Newton’s method and Halley’s method for the principal pth root of a matrix, Linear Alg. Appl. 432 (2010), no. 8, 1905–1922.
[25] N.J. Higham, Functions of matrices: theory and computation, vol. 104, Siam, 2008.
[26] B. Iannazzo, On the Newton method for the matrix pth root, SIAM J. Matrix Anal. Appl. 28 (2006), no. 2, 503–523.
[27] G. Julia, Memoire sur l’iteration des fonctions rationnelles, J. Math. Pures Appl. 8 (1918), 47–245.
[28] L.V. Kantorovich, Functional analysis and applied mathematics, Uspekhi Mate. Nauk 3 (1948), no. 6, 89–185.
[29] S.K. Khattri, How to increase convergence order of the Newton method to 2×m?, Appl. Math. 59 (2014), no. 1,15–24.
[30] T. Liu, X. Qin, and P. Wang, Local convergence of a family of iterative methods with sixth and seventh order convergence under weak conditions, Int. J. Comput. Meth. 16 (2019), no. 08, 1850120.
[31] A.A. Magrenan Ruiz and I.K. Argyros, Two-step Newton methods, J. Complexity 30 (2014), no. 4, 533–553.
[32] M. Moccari and T. Lotfi, On a two-step optimal Steffensen-type method: Relaxed local and semi-local convergence analysis and dynamical stability, J. Math. Anal. Appl. 468 (2018), no. 1, 240–269.
[33] , Using majorizing sequences for the semi-local convergence of a high-order and multipoint iterative method along with stability analysis, J. Math. Exten. 15 (2020).
[34] P.J. Psarrakos, On the mth roots of a complex matrix, Electron. J. Linear Alg. 9 (2002), 32–41.
[35] J.R. Sharma, D. Kumar, I.K. Argyros, and A.A. Magre˜n´an, ´ On a bi-parametric family of fourth order composite newton–jarratt methods for nonlinear systems, Mathematics 7 (2019), no. 6, 492.
[36] W.T. Shaw, Complex analysis with Mathematica, Cambridge University Press, 2006.
[37] J.F. Traub, Iterative methods for the solution of equations, vol. 312, American Mathematical Soc., 1982.