Optimal two-parameter geometric and arithmetic mean bounds for the Sándor–Yang mean
نویسندگان
چکیده
منابع مشابه
Sharp Two Parameter Bounds for the Logarithmic Mean and the Arithmetic–geometric Mean of Gauss
For fixed s 1 and t1,t2 ∈ (0,1/2) we prove that the inequalities G(t1a + (1− t1)b,t1b+(1− t1)a)A1−s(a,b) > AG(a,b) and G(t2a+(1− t2)b,t2b+(1− t2)a)A1−s(a,b) > L(a,b) hold for all a,b > 0 with a = b if and only if t1 1/2− √ 2s/(4s) and t2 1/2− √ 6s/(6s) . Here G(a,b) , L(a,b) , A(a,b) and AG(a,b) are the geometric, logarithmic, arithmetic and arithmetic-geometric means of a and b , respectively....
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ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2019
ISSN: 1029-242X
DOI: 10.1186/s13660-019-2245-x