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On a Study of a Family of Higher-Order Recurrence Relations

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  • Mensah Folly-Gbetoula
  • Kgatliso Mkhwanazi
  • Darlison Nyirenda
  • Thanin Sitthiwirattham

Abstract

In this work, group theory is applied to obtain generators of the Lie algebra for a class of rational difference equations of order k+l where k and l are positive integers. This is followed by deriving invariants and solutions via some linear recurrences and with the introduction of some number-theoretic arithmetical functions. Furthermore, sufficient conditions for the existence of solutions for periods two and four are provided in special cases. The results in this paper generalize certain known results.

Suggested Citation

  • Mensah Folly-Gbetoula & Kgatliso Mkhwanazi & Darlison Nyirenda & Thanin Sitthiwirattham, 2022. "On a Study of a Family of Higher-Order Recurrence Relations," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-11, September.
    • Handle: RePEc:hin:jnlmpe:6770105
    DOI: 10.1155/2022/6770105
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