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We approximate zeros of nonlinear operator equations in Banach space setting using Newton-Kantrorvich assumptions and the majorant theory for the midpoint method.

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ARGYROS, I. K. (1999). AN ERROR ANALYSIS FOR THE MIDPOINT METHOD. Tamkang Journal of Mathematics, 30(2), 71–83.


M. Altman, Iterative methods of higher order, Bull. Acad. Polon. Sci. Ser. Math. Astr. Phys. 9(1961), 63-68.

I. K. Argyros, Quadratic equations and applications to Chandrasekhar's and related equations, Bull. Austral. Math. Soc. 32(1985), 275-292.

I. K. Argyros, On a class of nonlinear integral equations arising in neutron transport, Aequationes Mathematicae 36(1988), 94-111.

I. K. Argyros, On the solution of equations with nondifferentiable operators and the Ptak error estimates, BIT 90(1990), 752-754

I. K. Argyros, On the convergence of a Halley-Chebysheff-type method under Newton-Kantorovich hypotheses, Appl. Math. Letters 6(1993), 71-74.

I. K. Argyros and D. Chen, A note on the Halley method in Banach spaces, Appl. Math. and Comp. 58(1993), 215-224.

I. K. Argyros and D. Chen, On the midpoint iterative method for solving nonlinear operator equations and applications to the solution of integral equations, Mathematica-Revue D'analyse Numerique et de Theorid de l'approximation, Tome 23, fasc. 2(1994), 139-152.

I. K. Argyros and F. Szidarovszky, On the monotone convergence of general Newton-like methods, Bull. Austral. Math. Soc. 45(1992), 489-502.

I. K. Argyros and F. Szidarovszky, The Theory and Application of Iteration Methods, C. R. C. Press, Inc. Boca Raton, Florida, (1993).

S. Chandrasekhar, Radiative Transfer, Dover Publ., New York, 1960

X. Chen and T. Yamamoto, Convergence domains of certain iterative methods for solving nonlinear equation, Number. Funct. Anal. and Optimiz. 10(1989), 37-48.

S. Kanno, Convergence theorems for the method of tangent hyperbolas, Math Japonica 37(1992), 711-722.

L. V. Kantorovich and G. P. Akilov, Functional Analysis in Normed Spaces, Pergamon Press, New York, 1964.

M. A. Mertvecova, An analog of the process of tangent hyperbolas for general functional equations (Russian), Dokl. Akad. Nauk. SSSR. 88(1953), 611-614.

M. T. Necepurenko, On Chebysheff's method for functional equations (Russian), Usephi Mat. Nauk. 9(1954), 163-170.

F. A. Potra and V. Ptak, Sharp error bounds for Newton's process, Numer. Math. 34(1980), 63-72.

F. A. Potra, On an iterative algorithm of order 1.839... for solving nonlinear operator equations, Numer. Funct. Anal. and Optimiz. 7(1984-85), 75-106.

R. A. Safiev, The method of tangent hyperbolas, Sov. Math. Dokl. 4(1963), 482-485

A. E. Taylor, Introduction to Functional Analysis, Wiley Publ. New York, 1957.

S. Ul'm, Iteration methods with divided differences of the second order (Russian), Dokl Akad. Nauk. SSSR 158(1964), 55-58. Soviet Math. Dokl. 5, 1187-1190.

T. Yamamoto, On the method of tangent hyperbolas in Banach spaces, J. Comput. Appl Math. 21(1988), 75-86.

P. P. Zabrejko and D. F. Nguen, The majorant method in the theory of Newton-Kantorovich approximations and the Ptak error estimates, Numer. Funct. Anal. and Optimiz. 9(1987), 671-684.

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