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Weighted Norms In Advanced Volterra Difference Equations

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Advances in Discrete Dynamical Systems, Difference Equations and Applications (ICDEA 2021)

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Abstract

In this research we explore the existence of bounded solutions, and periodic solutions of Advanced type Volterra difference equations of the form

$$\begin{aligned} x(n) = f(n, x(n), x(n -h)) -\sum ^{\infty }_{s=n}Q(s,x(s), x(s-h))C(n-s) + p(n) \end{aligned}$$

using weighted norms and the contraction mapping principle in a suitable space. The suitable space will be constructed based on the magnitude and properties of p and the convergence properties of the term C.

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Authors and Affiliations

  1. Department of Mathematics, University of Dayton, Dayton, OH, 45469-2316, USA

    Youssef N. Raffoul

Authors
  1. Youssef N. Raffoul
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Correspondence to Youssef N. Raffoul .

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Editors and Affiliations

  1. Department of Mathematics, Trinity University, San Antonio, TX, USA

    Saber Elaydi

  2. University of Rhode Island, Kingston, RI, USA

    Mustafa R. S. Kulenović

  3. University of Sarajevo, Sarajevo, Bosnia and Herzegovina

    Senada Kalabušić

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Raffoul, Y.N. (2023). Weighted Norms In Advanced Volterra Difference Equations. In: Elaydi, S., Kulenović, M.R.S., Kalabušić, S. (eds) Advances in Discrete Dynamical Systems, Difference Equations and Applications. ICDEA 2021. Springer Proceedings in Mathematics & Statistics, vol 416. Springer, Cham. https://doi.org/10.1007/978-3-031-25225-9_18

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