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Iterated convergence on Banach space valued functions of abstract g-fractional calculus

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Abstract

The novelty of this paper is the design of suitable iterative methods for generating a sequence approximating solutions of equations on Banach spaces. Applications of the semi-local convergence are suggested including Banach space valued functions of fractional calculus, where all integrals are of Bochner-type.

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References

  1. C.D. Aliprantis, K.C. Border, Infinite dimensional analysis (Springer, New York, 2006)

  2. S. Amat, S. Busquier, S. Plaza, J. Math. Anal. Appl. 366, 164 (2010)

    Article  MathSciNet  Google Scholar 

  3. G.A. Anastassiou, Rev. Proyecc. 36, 149 (2017)

    Article  Google Scholar 

  4. G.A. Anastassiou, Nonlinear Funct. Anal. Appl., accepted for publication (2018)

  5. G.A. Anastassiou, Principles of general fractional analysis for Banach space valued functions, submitted for publication (2018)

  6. I.K. Argyros, J. Math. Anal. Appl. 298, 374 (2004)

    Article  MathSciNet  Google Scholar 

  7. I.K. Argyros, A. Magrenan, Iterative methods and their dynamics with applications (CRC Press, New York, 2017)

  8. Bochner integral. Encyclopedia of mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Bochner_integral&oldid=38659

  9. M. Edelstein, J. Lond. Math. Soc. 37, 74 (1962)

    Article  MathSciNet  Google Scholar 

  10. J.A. Ezquerro, J.M. Gutierrez, M.A. Hernandez, N. Romero, M.J. Rubio, Gac. R. Soc. Mat. Esp. 13, 53 (2010)

    MathSciNet  Google Scholar 

  11. L.V. Kantorovich, G.P. Akilov, Functional analysis in normed spaces (Pergamon Press, New York, 1982)

  12. G.E. Ladas, V. Lakshmikantham, Differential equations in abstract spaces (Academic Press, New York, London, 1972)

  13. A. Magrenan, Appl. Math. Comput. 248, 215 (2014)

    MathSciNet  Google Scholar 

  14. J. Mikusinski, The Bochner integral (Academic Press, New York, 1978)

  15. F.A. Potra, V. Ptak, Nondiscrete induction and iterative processes (Pitman Publ., London, 1984)

  16. P.D. Proinov, J. Complex. 26, 3 (2010)

    Article  Google Scholar 

  17. G.E. Shilov, Elementary functional analysis (Dover Publications Inc., New York, 1996)

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Memphis, Memphis, TN, 38152, USA

    George A. Anastassiou

  2. Department of Mathematical Sciences, Cameron University, Lawton, OK, 73505, USA

    Ioannis K. Argyros

Authors
  1. George A. Anastassiou
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  2. Ioannis K. Argyros
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Correspondence to George A. Anastassiou.

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Anastassiou, G.A., Argyros, I.K. Iterated convergence on Banach space valued functions of abstract g-fractional calculus. Eur. Phys. J. Spec. Top. 226, 3667–3680 (2017). https://doi.org/10.1140/epjst/e2018-00023-5

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  • DOI: https://doi.org/10.1140/epjst/e2018-00023-5

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