New generalizations of Németh-Mohapatra type inequalities on time scales (Q1743160)

In recent papers, some classical inequalities have been extended to functions defined on time scales, that are closed subsets \(\mathbb T\) of \(\mathbb R\). Examples are \(\mathbb R\), \(\mathbb N\) when we obtain the classical integral and discrete versions; but there are others in use such as \(\{q^t: t\in \mathbb N_0, q>1\}\); see \textit{M. Bohner} and \textit{A. Peterson} [Dynamic equations on time scales. An introduction with applications. Basel: Birkhäuser (2001; Zbl 0978.39001)]. In this paper, time scale versions of the discrete inequalities of \textit{J. Németh} [Acta Sci. Math. 32, 295--299 (1971; Zbl 0226.26020)] and the analogous integral inequalities of \textit{R. N. Mohapatra} and \textit{D. C. Russell} [Aequationes Math. 28, 199--207 (1985; Zbl 0573.26010)] are proved. The results are used to obtain new generalisations of several classical inequalities.