Generalized g-fractional calculus and iterative methods
Keywords:
Generalized Banach space, semilocal convergence, g-fractional calculus.Abstract
We approximated solutions of some iterative methods on a generalized Banach space setting in [5]. Earlier studies such as [7-12] the operator involved is Frechet-differentiable. In [5] we assumed that the operator is only continuous. This way we extended the applicability of these methods to include generalized fractional calculus and problems from other areas. In the present study applications include generalized g-fractional calculus. Fractional calculus is very important for its applications in many applied sciences.
Mathematics Subject Classiffcation (2010): 26A33, 65G99, 47J25.
References
Amat, S., Busquier, S., Plaza, S., Chaotic dynamics of a third-order Newton-type method, J. Math. Anal. Appl., 366(2010), no. 1, 164-174.
Anastassiou, G., Fractional Differentiation Inequalities, Springer, New York, 2009.
Anastassiou, G., Fractional representation formulae and right fractional inequalities, Mathematical and Computer Modelling, 54(2011), no. 11-12, 3098-3115.
Anastassiou, G., Advanced fractional Taylor's formula, J. Comput. Anal. Appl., 21(7)(2016), 1185-1204.
Anastassiou, G., Argyros, I.K., Convergence for iterative methods on Banach spaces of convergence structure with applications in fractional calculus, SeMA, DOI 10.1007/s40324-015-0044-y.
Argyros, I.K., Newton-like methods in partially ordered linear spaces, J. Approx. Th. Appl., 9(1993), no. 1, 1-10.
Argyros, I.K., Results on controlling the residuals of perturbed Newton-like methods on Banach spaces with a convergence structure, Southwest J. Pure Appl. Math., 1(1995), 32-38.
Argyros, I.K., Convergence and Applications of Newton-type iterations, Springer-Verlag, New York, 2008.
Ezquerro, J.A., Gutierrez, J.M., Hernandez, M.A., Romero, N., Rubio, M.J., The Newton method: From Newton to Kantorovich (Spanish), Gac. R. Soc. Mat. Esp., 13(2010), 53-
Magrenan, A.A., Different anomalies in a Surrutt family of iterative root finding methods, Appl. Math. Comput., 233(2014), 29-38.
Magrenan, A.A., A new tool to study real dynamics: The convergence plane, Appl. Math. Comput., 248(2014), 215-224.
Meyer, P.W., Newton's method in generalized Banach spaces, Numer. Func. Anal. Optimiz., 9(1987), no. 3 and 4, 244-259.
Mukeen, S., Habibullah, G.M., k-Fractional integrals and Application, Int. J. Contemp. Math. Sciences, 7(2012), no. 2, 89-94.
Potra, F.A., Ptak, V., Nondiscrete induction and iterative processes, Pitman Publ., London, 1984.
Zekisarikaya, M., Karaca, A., On the Riemann-Liouville fractional integral and applications, Intern. J. Stat. and Math., 1(2014), no. 3, 33-43.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2016 Studia Universitatis Babeș-Bolyai Mathematica
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
