# Some more results on a generalized `useful' R-norm information measure

## Main Article Content

## Abstract

A parametric mean length is defined as the quantity

$$ _{R\beta} L_u = \frac{R}{R-1} \Bigg [1 - \sum P_i^\beta \bigg (\frac{u_i}{ \sum u_ip_i^\beta}\bigg )^{\frac{1}{R}} D^{-n_i \Big (\frac{R-1}{R}\Big )}\Bigg ], $$

where $R>0$ ($\not=1$), $\sum p_i=1$. This being the useful mean length of code words weighted by utilities, $u_i$. Lower and upper bounds for $_{R\beta} L_u$ are derived in terms of `useful'-R-norm information measure for the incomplete power distribution, $p^\beta$.

$$ _{R\beta} L_u = \frac{R}{R-1} \Bigg [1 - \sum P_i^\beta \bigg (\frac{u_i}{ \sum u_ip_i^\beta}\bigg )^{\frac{1}{R}} D^{-n_i \Big (\frac{R-1}{R}\Big )}\Bigg ], $$

where $R>0$ ($\not=1$), $\sum p_i=1$. This being the useful mean length of code words weighted by utilities, $u_i$. Lower and upper bounds for $_{R\beta} L_u$ are derived in terms of `useful'-R-norm information measure for the incomplete power distribution, $p^\beta$.

## Article Details

How to Cite

Kumar, S. (2009). Some more results on a generalized `useful’ R-norm information measure.

*Tamkang Journal of Mathematics*,*40*(2), 211–216. https://doi.org/10.5556/j.tkjm.40.2009.469
Issue

Section

Papers