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On the Application of Ergodic Theory to an Alternating Series Expansion for Real Numbers

In: Exploring Mathematical Analysis, Approximation Theory, and Optimization

Author

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  • Chryssoula Ganatsiou

    (University of Thessaly, Gaiopolis)

  • Ilias K. Savvas

    (University of Thessaly, Gaiopolis)

Abstract

By considering a general alternating series algorithm introduced by A. and J. Knopfmacher according to which every real number may be expressed by alternating series representations in terms of rationals we present some important results arising from the application of ergodic theory to an alternating series expansion for real numbers in terms of rationals generating from another algorithm called alternating Sylvester-Engel-Lüroth series expansion (alternating SEL series expansion) which gives generalized versions of the corresponding three alternating series expansions constructing from the general alternating series algorithm of A. and J. Knopfmacher.

Suggested Citation

  • Chryssoula Ganatsiou & Ilias K. Savvas, 2023. "On the Application of Ergodic Theory to an Alternating Series Expansion for Real Numbers," Springer Optimization and Its Applications, in: Nicholas J. Daras & Michael Th. Rassias & Nikolaos B. Zographopoulos (ed.), Exploring Mathematical Analysis, Approximation Theory, and Optimization, pages 85-100, Springer.
    • Handle: RePEc:spr:spochp:978-3-031-46487-4_6
    DOI: 10.1007/978-3-031-46487-4_6
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    11K55; 37A25; 37A30; 37A50; 37A10; 60A10;
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