Abstract
Explicit iterative methods have been used extensively to generate a sequence approximating a solution of an equation on a Banach space setting.
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C.D. Aliprantis, K.C. Border, Infinite Dimensional Analysis (Springer, New York, 2006)
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.A. Anastassiou, Strong right fractional calculus for banach space valued functions. Revis. Proyecc. 36(1), 149–186 (2017)
G.A. Anastassiou, A strong fractional calculus theory for banach space valued functions, in Nonlinear Functional Analysis and Applications (Korea) (2017). accepted for publication
G.A. Anastassiou, I.K. Argyros, Iterative methods and their applications to Banach space valued functions in abstract fractional calculus, in Progress in Fractional Differentiation and Applications (2017). accepted
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, A. Magréñan, Iterative Methods and their Dynamics with Applications (CRC Press, New York, 2017)
Bochner integral, Encyclopedia of Mathematics, http://www.encyclopediaofmath.org/index.php?title=Bochner_integral&oldid=38659
M. Edelstein, On fixed and periodic points under contractive mappings. J. Lond. Math. Soc. 37, 74–79 (1962)
J.A. Ezquerro, J.M. Gutierrez, M.A. Hernandez, N. Romero, M.J. Rubio, The Newton method: from Newton to Kantorovich (Spanish). Gac. R. Soc. Mat. Esp. 13, 53–76 (2010)
L.V. Kantorovich, G.P. Akilov, Functional Analysis in Normed Spaces (Pergamon Press, New York, 1982)
A. Magréñan, A new tool to study real dynamics: the convergence plane. Appl. Math. Comput. 248, 215–224 (2014)
J. Mikusinski, The Bochner integral (Academic Press, New York, 1978)
F.A. Potra, V. Ptăk, Nondiscrete Induction and Iterative Processes (Pitman Publ, 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)
G.E. Shilov, Elementary Functional Analysis (Dover Publications Inc, New York, 1996)
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Anastassiou, G.A., Argyros, I.K. (2018). Explicit-Implicit Methods with Applications to Banach Space Valued Functions in Abstract Fractional Calculus. In: Functional Numerical Methods: Applications to Abstract Fractional Calculus. Studies in Systems, Decision and Control, vol 130. Springer, Cham. https://doi.org/10.1007/978-3-319-69526-6_1
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DOI: https://doi.org/10.1007/978-3-319-69526-6_1
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