Companion inequalities for certain bivariate means

Neuman, Edward; Sándor, József

doi:10.2298/aadm0901046n

Cited by 17 publications

(6 citation statements)

References 13 publications

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“…is due to Yang [33] (see also [46]). Now we present a more general results involving identric (exponential) mean and power mean.…”

Section: New Sharp Inequalities For Identric (Exponential) Meanmentioning

confidence: 99%

A new way to prove L'Hospital Monotone Rules with applications

Yang¹

2014

Preprint

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Let −∞ ≤ a < b ≤ ∞. Let f and g be differentiable functions on (a, b) and let g ′ = 0 on (a, b). By introducing an auxiliary function H f,g := (f ′ /g ′ ) g − f , we easily prove L'Hoipital rules for monotonicity. This offer a natural and concise way so that those rules are easier to be understood. Using our L'Hospital Piecewise Monotone Rules (for short, LPMR), we establish three new sharp inequalities for hyperbolic and trigonometric functions as well as bivariate means, which supplement certain known results.

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“…is due to Yang [33] (see also [46]). Now we present a more general results involving identric (exponential) mean and power mean.…”

Section: New Sharp Inequalities For Identric (Exponential) Meanmentioning

confidence: 99%

A new way to prove L'Hospital Monotone Rules with applications

Yang¹

2014

Preprint

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“…Recently, the Schwab-Borchardt mean and its generated means have been the subject intensive research. In particular, many remarkable inequalities for these means can be found in the literature [1][2][3][4][5][8][9][10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Optimal Bounds for Neuman Mean Using Arithmetic and Centroidal Means

Song

Qian

Chu

2016

Journal of Function Spaces

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We present the best possible parametersα1,α2,β1,β2∈Randα3,β3∈(1/2,1)such that the double inequalitiesα1A(a,b)+(1-α1)C(a,b)<NQA(a,b)<β1A(a,b)+(1-β1)C(a,b),Aα2(a,b)C1-α2(a,b)<NQA(a,b)<Aβ2(a,b)C1-β2(a,b),andC[α3a+(1-α3)b,α3b+(1-α3)a]<NQA(a,b)<C[β3a+(1-β3)b,β3b+(1-β3)a]hold for alla,b>0witha≠band give several sharp inequalities involving the hyperbolic and inverse hyperbolic functions. Here,N(a,b),A(a,b),Q(a,b), andC(a,b)are, respectively, the Neuman, arithmetic, quadratic, and centroidal means ofaandb, andNQA(a,b)=N[Q(a,b),A(a,b)].

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“…hold for all , > 0 with ̸ = . Neuman and Sándor [15] and Gao [20] proved that 1 = 1, 1 = /2, 2 = 1, 2 = 2 √ 2/ , 3 = 1, 3 = 3/ , 4 = / , 4 = 1, 5 = 1, and 5 = 2 / are the best possible constants such that the double inequalities In [34], Sándor established that…”

Section: Introductionmentioning

confidence: 99%