2013
DOI: 10.1155/2013/903982
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Abstract: We give the greatest valuesr1,r2and the least valuess1,s2in (1/2, 1) such that the double inequalitiesC(r1a+(1-r1)b,r1b+(1-r1)a)<αA(a,b)+(1-α)T(a,b)<C(s1a+(1-s1)b,s1b+(1-s1)a)andC(r2a+(1-r2)b,r2b+(1-r2)a)<αA(a,b)+(1-α)M(a,b)<C(s2a+(1-s2)b,s2b+(1-s2)a)hold for anyα∈(0,1)and alla,b>0witha≠b, whereA(a,b),M(a,b),C(a,b),andT(a,b)are the arithmetic, Neuman-Sándor, contraharmonic, and second Seiffert means ofaandb, respectively.