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On the solutions of a second-order difference equation in terms of generalized Padovan sequences

  • Yacine Halim EMAIL logo und Julius Fergy T. Rabago
Veröffentlicht/Copyright: 18. Mai 2018
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Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 68 Heft 3

Abstract

This paper deals with the solution, stability character and asymptotic behavior of the rational difference equation

xn+1=αxn−1+βγxnxn−1,n∈N0,

where ℕ0 = ℕ ∪ {0}, α, β, γ ∈ ℝ+, and the initial conditions x–1 and x0 are non zero real numbers such that their solutions are associated to generalized Padovan numbers. Also, we investigate the two-dimensional case of the this equation given by

xn+1=αxn−1+βγynxn−1,yn+1=αyn−1+βγxnyn−1,n∈N0.
MSC 2010: Primary 39A10; Secondary 40A05
Keywords: difference equations; general solution; stability; generalized Padovan numbers

This work was supported by LMAM Laboratory, Jijel University.

Communicated by Michal Fečkan

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Received: 2017-4-23
Accepted: 2017-11-5
Published Online: 2018-5-18
Published in Print: 2018-6-26

© 2018 Mathematical Institute Slovak Academy of Sciences

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  28. On the solutions of a second-order difference equation in terms of generalized Padovan sequences
  30. Fixed points in C∗-algebra valued b-metric spaces endowed with a graph
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https://doi.org/10.1515/ms-2017-0130
Schlagwörter für diesen Artikel
difference equations; general solution; stability; generalized Padovan numbers

Artikel in diesem Heft

  2. Small-large subgroups of the reals
  4. Structural properties of algebras of S-probabilities
  6. Approximation in quantum measure spaces
  8. On Fibonomial sums identities with special sign functions: analytically q-calculus approach
  10. On the proximity of multiplicative functions to the number of distinct prime factors function
  12. Truncated euler polynomials
  14. Growth series of crossed and two-sided crossed products of cyclic groups
  16. Weakly U-abundant semigroups with strong Ehresmann transversals
  18. Iterative learning control with pulse compensation for fractional differential systems
  20. Rectifiable and nonrectifiable solution curves of half-linear differential systems
  22. Uniqueness properties of meromorphic functions in the light of three shared sets
  24. A new family of analytic functions defined by means of Rodrigues type formula
  26. Perturbation analysis of a nonlinear equation arising in the Schaefer-Schwartz model of interest rates
  28. On the solutions of a second-order difference equation in terms of generalized Padovan sequences
  30. Fixed points in C∗-algebra valued b-metric spaces endowed with a graph
  32. A general fixed point theorem for two pairs of mappings satisfying a mixed implicit relation
  34. Productively sequential spaces
  36. Euler classes of vector bundles over iterated suspensions of real projective spaces
  38. The stationary distribution and ergodicity of a stochastic mutualism model
  40. Restricted injective dimensions over local homomorphisms
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