Monotonicity and convexity for nabla fractional \((q,h)\)-differences. (English) Zbl 1364.39009
The authors study the monotonicity and convexity of the nabla fractional \((q,h)\)-difference operator. Furthermore, they show that if the \(\alpha\)th-order nabla fractional \((q,h)\)-difference is positive, then the \(N\)th-order nabla fractional \((q,h)\)-difference is positive, where \(N-1<\alpha\leq N\), \(N=1,2\), that is the \(\alpha\)th-order nabla fractional \((q,h)\)-difference has a strong connection to the monotonicity and convexity.
Reviewer: Thanin Sitthiwirattham (Bangkok)
MSC:
| 39A13 | Difference equations, scaling (\(q\)-differences) |
| 39A12 | Discrete version of topics in analysis |
| 39A70 | Difference operators |
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