Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
121 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

A monotonicity result for the $q-$fractional operator (1602.07713v1)

Published 24 Feb 2016 in math.CA

Abstract: In this article we prove that if the $q-$fractional operator $(~{q}\nabla{qa}\alpha y)(t)$ of order $0<\alpha\leq 1$ , $0<q\<1$ and starting at some $qa \in T_q=\{q^k: k \in \mathbb{Z}\}\cup \{0\},~~a\>0$ is positive such that $y(a) \geq 0$, then $y(t)$ is $c_q(\alpha)-$increasing, $c_q(\alpha)=\frac{1-q\alpha}{1-q}q{1-\alpha}$. Conversely, if y(t) is increasing and $y(a)\geq 0$, then $(~{q}\nabla{qa}\alpha y)(t)\geq 0$. As an application, we proved a $q-$fractional version of the Mean-Value Theorem.

Summary

We haven't generated a summary for this paper yet.