Generalizing Taylor Expansion Series Through Succeeding Initial Value Problems

  1. M. Fernández-Martínez 1
  2. J. L. G. Guirao 2
  1. 1 Centro Universitario de la Defensa
  2. 2 Universidad Politécnica de Cartagena
    info

    Universidad Politécnica de Cartagena

    Cartagena, España

    ROR https://ror.org/02k5kx966

Journal:
Qualitative theory of dynamical systems

ISSN: 1575-5460

Year of publication: 2017

Volume: 16

Issue: 1

Pages: 71-100

Type: Article

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Abstract

In this paper, the classical Taylor’s expansion series for a given continuous and k-times differentiable real function is obtained as the unique solution of a certain class of initial value problems. Further, through some subsequent generalizations regarding that problem in terms of certain derivative-based operators, we obtain some generalized Taylor’s type polynomial expansions, including the Taylor–Aleph series, which remains as particular cases. In addition to that, some analytical properties about these involved operators are also provided.

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