Best Possible Inequalities among Harmonic, Geometric, Logarithmic and Seiffert Means
نویسندگان
چکیده
In this paper, we find the greatest value α and the least values β , p , q and r in (0,1/2) such that the inequalities L(αa+ (1−α)b,αb+ (1−α)a) < P(a,b) < L(βa + (1− β)b,βb + (1− β)a) , H(pa + (1− p)b, pb + (1− p)a) > G(a,b) , H(qa+ (1− q)b,qb +(1− q)a) > L(a,b) , and G(ra+(1− r)b,rb+(1− r)a) > L(a,b) hold for all a,b > 0 with a = b . Here, H(a,b) , G(a,b) , L(a,b) and P(a,b) denote the harmonic, geometric, logarithmic and Seiffert means of two positive numbers a and b , respectively. Mathematics subject classification (2010): 26E60.
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