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Sharp bounds for Seiffert and Neuman-Sándor means in terms of generalized logarithmic means

Research paper by Yu-Ming Chu, Bo-Yong Long, Wei-Ming Gong, Ying-Qing Song

Indexed on: 07 Jan '13Published on: 07 Jan '13Published in: Journal of Inequalities and Applications



Abstract

In this paper, we prove three sharp inequalities as follows: P(a,b)>L2(a,b)Open image in new window, T(a,b)>L5(a,b)Open image in new window and M(a,b)>L4(a,b)Open image in new window for all a,b>0Open image in new window with a≠bOpen image in new window. Here, Lr(a,b)Open image in new window, M(a,b)Open image in new window, P(a,b)Open image in new window and T(a,b)Open image in new window are the r th generalized logarithmic, Neuman-Sándor, first and second Seiffert means of a and b, respectively.MSC:26E60.