Abstract
We introduce a fixed point iterative scheme and use it to approximate a solution of a nonlinear operator equation. Applications are suggested involving in particular right multivariate fractional calculus. It follows [8].
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References
S. Amat, S. Busquier, S. Plaza, Chaotic dynamics of a third-order Newton-type method. J. Math. Anal. Appl. 366(1), 164–174 (2010)
G. Anastassiou, Fractional Differentiation Inequalities (Springer, New York, 2009)
G. Anastassiou, Fractional representation formulae and right fractional inequalities. Math. Comput. Model. 54(10–12), 3098–3115 (2011)
G. Anastassiou, Intelligent Mathematics: Computational Analysis (Springer, Heidelberg, 2011)
G. Anastassiou, Advanced Inequalities (World Scientific Publ. Corp, Singapore, 2011)
G. Anastassiou, On right multidimensional Riemann-Liouville fractional integral. J. Comput. Anal. Appl. (2015)
G. Anastassiou, I.K. Argyros, Intelligent Numerical Methods: Applications to Fractional Calculus, Studies in Computational Intelligence (Springer, Heidelberg, 2016)
G. Anastassiou, I. Argyros, Fixed point schemes with applications in right multivariate fractional calculus. submitted for publication (2015)
I.K. Argyros, A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space. J. Math. Anal. Appl. 298, 374–397 (2004)
I.K. Argyros, Convergence and Applications of NewtonType Iterations (Springer, New York, 2008)
I.K. Argyros, On a class of Newton-like methods for solving nonlinear equations. J. Comput. Appl. Math. 228, 115–122 (2009)
I.K. Argyros, A semilocal convergence analysis for directional Newton methods. AMS J. 80, 327–343 (2011)
I.K. Argyros, Y.J. Cho, S. Hilout, Numerical Methods for Equations and Its Applications (CRC Press/Taylor and Fracncis, New York, 2012)
I.K. Argyros, S. Hilout, Weaker conditions for the convergence of Newton’s method. J. Complex. 28, 364–387 (2012)
J.A. Ezquérro, J.M. Gutiérrez, M.A. Hernández, N. Romero, M.J. Rubio, The Newton method: from Newton to Kantorovich (Spanish). Gac. R. Soc. Mat. Esp. 13, 53–76 (2010)
J.A. Ezquérro, M.A. Hernández, Newton-type methods of high order and domains of semilocal and global convergence. Appl. Math. Comput. 214(1), 142–154 (2009)
L.V. Kantorovich, G.P. Akilov, Functional Analysis in Normed Spaces (Pergamon Press, New York, 1964)
A.A. Magreñán, Different anomalies in a Jarratt family of iterative root finding methods. Appl. Math. Comput. 233, 29–38 (2014)
A.A. Magreñán, A new tool to study real dynamics: the convergence plane. Appl. Math. Comput. 248, 215–224 (2014)
F.A. Potra, V. Ptak, Nondiscrete Induction and Iterative Processes (Pitman, London, 1984)
P.D. Proinov, New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems. J. Complex. 26, 3–42 (2010)
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Anastassiou, G.A., Argyros, I.K. (2016). Fixed Point Results and Their Applications in Right Multivariate Fractional Calculus. In: Intelligent Numerical Methods II: Applications to Multivariate Fractional Calculus. Studies in Computational Intelligence, vol 649. Springer, Cham. https://doi.org/10.1007/978-3-319-33606-0_2
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DOI: https://doi.org/10.1007/978-3-319-33606-0_2
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