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Stability Criterion for Volterra Type Delay Difference Equations Including a Generalized Difference Operator

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The stability of a class of Volterra-type difference equations that include a generalized difference operator ∆_a is investigated using Krasnoselskii’s fixed point theorem and some results are obtained. In addition, some examples are given to illustrate our theoretical results.

Abstract

The stability of a class of Volterra-type difference equations that include a generalized difference operator ∆_a is investigated using Krasnoselskii’s fixed point theorem and some results are obtained. In addition, some examples are given to illustrate our theoretical results.

참고문헌 (9)

  1. R. P. Agarwal, "Difference equations and inequalities: theory, methods and applications" (2000), Marcel Dekker, Inc.
  2. S. Elaydi, "An introduction to difference equations" (2005), Springer
  3. M. N. Islam, "Boundedness and stability in nonlinear delay difference equations employing fixed point theory", Electron. J. Qual. Theory Differ. Equ., 26, pp.18~ (2005)
  4. W. G. Kelley, "Difference equations: an introduction with applications" (1991), Academic Press
  5. T. M. Khandaker, "Stability properties of linear Volterra discrete systems with nonlinear perturbation", J. Difference Equ. Appl, 8, pp.857~874 (2002)
  6. R. E. Mickens, "Difference equations: theory and applications" (1991), Chapman and Hall
  7. M. Migda, "Boundedness and stability of discrete Volterra equations", Adv. Difference Equ., 47, pp.11~ (2015)
  8. D. R. Smart, "Fixed point theorems" (1980), Cambridge University Press
  9. E. Yankson, "Stability of Volterra difference delay equations", Electron. J. Qual. Theory Differ. Equ., 20, pp.14~ (2006)

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