Journal of Applied Sciences1812-56541812-5662Asian Network for Scientific Information10.3923/jas.2011.2866.2869KumarSatish ChoudharyArun 1220111115In this study, we study one parametric generalization measure of H (P) and H (P; Q). For the measure H (P; Q) we give three different kind of generalizations. These generalizations are R-Norm entropy and R-Norm inaccuracies. The Shannon-Gibbs type inequality has been generalized in different way using Holders inequality for R-Norm information measure and three different kinds of inaccuracy.]]>Boekee, D.E. and J.C.A. van der Lubbe,198045136155Campbell, L.L.,19658423429Daroczy, Z.,1970163636Haouas, A., B. Djebbar and R. Mekki,2008837433747Havrda, J.F. and F. Charvat,196733035Kerridge, D.F.,196123184194Kumar, S. and A. Choudhary,201148189Nath, P. and D.P. Mittal,197323439445Renyi, A.,19611547561Shannon, C.E.,194827379423Shisha, O.,1967Van der Lubbe, J.C.A.,19781978pp: 253266Van der Lubbe, J.C.A.,19811981Wang, Y.,201110461469Yan, R. and Q. Zheng,2009811801188Zheng, Y., Z. Qin, L. Shao and X. Hou,20087930935Arimoto, S.,197119181194