A pathological property of nonlocal discrete operators
Abstract
We demonstrate that there exist sequences { u n } n = 0 ∞ ⊆ ( 0 , + ∞ ) \big \{ u_{n} \big \}_{n = 0}^{\infty } \subseteq (0, +\infty ) such that u n + 1 > u n u_{n + 1}> u_{n} for each n ∈ N 0 n\in \mathbb {N}_{0} , but yet the fractional difference of the sequence is uniformly negative. This demonstrates a pathological property of nonlocal discrete operators.
Fields of Study & Subjects
Nonlinear Differential Equations Analysis
Fractional Differential Equations Solutions
Mathematical Inequalities and Applications
Publication details
- Journal / source
- Proceedings of the American Mathematical Society Series B
- Volume
- 13
- Issue
- 3
- Pages
- 20–34
- Publication date
- 7 January 2026
- Language
- EN