On the local convergence of modified Homeier-like method in Banach spaces
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 21 (2018) no. 4, pp. 419-433.

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The aim of this article is to investigate the local convergence analysis of the multi-step Homeier-like approach in order to approximate the solution of nonlinear equations in Banach spaces, which fulfilled the Lipschitz as well as Hölder continuity condition. The Hölder condition is more relaxer than Lipschitz condition. Also, the existence and uniqueness theorem has been derived and found their error bounds. Numerical examples are available to appear the importance of theoretical discussions.
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B. Panday; J. P. Jaiswal. On the local convergence of modified Homeier-like method in Banach spaces. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 21 (2018) no. 4, pp. 419-433. http://geodesic.mathdoc.fr/item/SJVM_2018_21_4_a5/

[1] Sharma J. R., Arora H., “A new family of optimal eighth order methods with dynamics for nonlinear equations”, Appl. Math. Comput., 273 (2016), 924–933 | MR

[2] Amat S., Busquier S., Plaza S., “Chaotic dynamics of a third-order Newton-type method”, J. Math. Anal. Appl., 366 (2010), 24–32 | DOI | MR | Zbl

[3] Behl R., Motsa S. S., “Geometric construction of eighth-order optimal families of Ostrowski's method”, Sci. World J., 2015 (2015), Article ID 614612 | DOI

[4] Argyros I. K., Hilout S., Computational Methods in Nonlinear Analysis, World Scientific Publishing Company, New Jersey, 2013 | MR | Zbl

[5] Traub J. F., Iterative Methods for the Solution of Equations, Prentice-Hall, Englewood Cliffs, New Jersey, 1964 | MR | Zbl

[6] Rall L. B., Schwetlick H., “Computational solution of nonlinear operator equations”, J. Appl. Math. Mech., 52 (1972), 630–631

[7] Amat S., Busquier S., Gutierrez J. M., “Geometric constructions of iterative functions to solve nonlinear equations”, J. Comp. Appl. Math., 157 (2003), 197–205 | DOI | MR | Zbl

[8] Argyros I. K., Computational Theory of Iterative Methods, Studies in computational mathematics, 15, Elsevier, New York, 2007 | MR | Zbl

[9] Chun C., Stanica P., Neta B., “Third-order family of methods in Banach spaces”, Comp. Math. Appl., 61 (2011), 1665–1675 | DOI | MR | Zbl

[10] Ortega J. M., Rheinboldt W. C., Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970 | MR | Zbl

[11] Argyros I. K., Khattri S. K., “Local convergence for a family of third order methods in Banach spaces”, Punjab Univ. J. Math., 46 (2016), 52–63 | MR

[12] Argyros I. K., George S., “Local convergence of two competing third order methods in Banach space”, Appl. Math., 41 (2016), 341–350 | MR

[13] Argyros I. K., Gonzalez D., Khattri S. K., “Local convergence of a one parameter fourth-order Jarratt-type method in Banach spaces”, Comment. Math. Univ. Carolin., 57 (2016), 289–300 | MR | Zbl

[14] Cordero A., Ezquerro J. A., Hernandez-Veron M. A., Torregrosa J. R., “On the local convergence of a fifth-order iterative method in Banach spaces”, Appl. Math. Comput., 251 (2015), 396–403 | MR | Zbl

[15] Polyanin A. D., Manzhirov A. V., Handbook of Integral Equations, CRC Press, Boca Raton, 1998 | MR | Zbl

[16] Martinez E., Singh S., Hueso J. L., Gupta D. K., “Enlarging the convergence domain in local convergence studies for iterative methods in Banach spaces”, Appl. Math. Comput., 281 (2016), 252–265 | MR

[17] Singh S., Gupta D. K., Martinez E., Hueso J. L., “Semilocal and local convergence of a fifth order iteration with Frechet derivative satisfying Holder condition”, Appl. Math. Comput., 276 (2016), 266–277 | MR

[18] Argyros I. K., George S., “Local convergence for some high convergence order Newton-like methods with frozen derivatives”, SeMA J., 70 (2015), 47–59 | DOI | MR | Zbl

[19] Wang X., Kou J., “Convergence for a class of multi-point modified Chebyshev–Halley methods under the relaxed conditions”, Numer. Algor., 68 (2015), 569–583 | DOI | MR | Zbl

[20] Argyros I. K., Magrenan A. A., “A study on the local convergence and the dynamics of Chebyshev–Halley-type methods free from second derivative”, Numer. Algor., 71 (2016), 1–23 | DOI | MR | Zbl

[21] Argyros I. K., George S., “Local convergence of deformed Halley method in Banach space under Holder continuity conditions”, J. Nonlinear Sci. Appl., 8 (2015), 246–254 | DOI | MR | Zbl

[22] Argyros I. K., George S., “Local convergence for deformed Chebyshev-type method in Banach space under weak conditions”, Cogent Math., 2 (2015), 1–12 | DOI | MR | Zbl

[23] Argyros I. K., George S., “Local convergence of modified Halley-like methods with less computation of inversion”, Novi Sad J. Math., 45 (2015), 47–58 | DOI | MR | Zbl

[24] George S., Argyros I. K., “A unified local convergence for Jarratt-type methods in Banach space under weak conditions”, Thai J. Math., 13:1 (2015), 165–176 | MR | Zbl

[25] Sharma J. R., Gupta P., “An efficient fifth order method for solving systems of nonlinear equations”, Comp. Math. Appl., 67 (2014), 591–601 | DOI | MR | Zbl

[26] Homeier H. H. H., “A modified Newton method with cubic convergence: the multivariate case”, J. Comp. Appl. Math., 169 (2004), 161–169 | DOI | MR | Zbl