Opial inequality in q-calculus

J Inequal Appl. 2018;2018(1):347. doi: 10.1186/s13660-018-1928-z. Epub 2018 Dec 14.

Abstract

In this article we give q-analogs of the Opial inequality for q-decreasing functions. Using a closed form of the restricted q-integral (see Gauchman in Comput. Math. Appl. 47:281-300, 2004), we establish a new integral inequality of the q-Opial type.

Keywords: Opial’s inequality; q-derivative; q-integral.