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Iterative Convergence with Banach Space Valued Functions in Abstract Fractional Calculus Cover

Iterative Convergence with Banach Space Valued Functions in Abstract Fractional Calculus

Open Access
|Dec 2017

References

  1. [1] C.D. Aliprantis and K.C. Border, Infinite Dimensional Analysis, Springer, New York, 2006.
  2. [2] S. Busquier S. Amat S. Plaza, Chaotic dynamics of a third-order Newton-type method, J. Math. Anal. Applic., 366(1), (2010), 164-174.10.1016/j.jmaa.2010.01.047
  3. [3] G.A. Anastassiou, A strong Fractional Calculus Theory for Banach space valued functions, Nonlinear Functional Analysis and Applications (Korea), accepted for publication, (2017)10.4067/S0716-09172017000100009
  4. [4] G.A. Anastassiou, Principles of general fractional analysis for Banach space valued functions, submitted for publication, (2017)10.1007/978-3-319-66936-6_4
  5. [5] 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, (2004), 374–397.10.1016/j.jmaa.2004.04.008
  6. [6] A. Magrenan I.K. Argyros, Iterative methods and their dynamics with applications, CRC Press, New York, 2017.
  7. [7] Encyclopedia of Mathematics, Bochner integral, URL: http://www.encyclopediaofmath.org/index.php?title=Bochner_integral&oldid=38659
  8. [8] M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc., 37, (1962), 74–79.10.1112/jlms/s1-37.1.74
  9. [9] J.M. Gutierrez J.A. Ezquerro M.A. Hernandez, The Newton method: From Newton to Kantorovich (Spanish), Gac. R. Soc. Mat. Esp., 13, (2010), 53–76.
  10. [10] G.P. Akilov L.V. Kantorovich, Functional Analysis in Normed Spaces, Pergamon Press, New York, 1982.10.1016/B978-0-08-023036-8.50010-2
  11. [11] G.E. Ladas and V. Lakshmikantham, Differential equations in abstract spaces, Academic Press, New York, London, 1972
  12. [12] S. Maruster, Ann. West. Univ. Timisoara, Math. and Comput. Sci., 54, (1), (2016), 1–9.10.1515/awutm-2016-0009
  13. [13] J. Mikusinski, The Bochner integral, Academic Press, New York, 1978.10.1007/978-3-0348-5567-9
  14. [14] V. Ptak F.A. Potra, Nondiscrete induction and iterative processes, Pitman Publ., London, 1984.
  15. [15] P.D. Proinov, New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems, J. Complexity, 26, (2010), 3–42.10.1016/j.jco.2009.05.001
  16. [16] G.E. Shilov, Elementary Functional Analysis, Dover Publications, Inc., New York, 1996.
DOI: https://doi.org/10.1515/awutm-2017-0012 | Journal eISSN: 1841-3307 | Journal ISSN: 1841-3293
Language: English
Page range: 17 - 31
Submitted on: May 1, 2017
Accepted on: Aug 3, 2017
Published on: Dec 29, 2017
Published by: West University of Timisoara
In partnership with: Paradigm Publishing Services
Publication frequency: Volume open

© 2017 George A. Anastassiou, Ioannis K. Argyros, published by West University of Timisoara
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.