Bivariate Means Research Articles

Multivariable generalizations of bivariate means via invariance

AbstractFor a given p-variable mean $$M :I^p \rightarrow I$$ M : I p → I (I is a subinterval of $${\mathbb {R}}$$ R ), following (Horwitz in J Math Anal Appl 270(2):499–518, 2002) and (Lawson and Lim in Colloq Math 113(2):191–221, 2008), we can define (under certain assumptions) its $$(p+1)$$ ( p + 1 ) -variable $$\beta $$ β -invariant extension as the unique solution $$K :I^{p+1} \rightarrow I$$ K : I p + 1 → I of the functional equation $$\begin{aligned}&K\big (M(x_2,\dots ,x_{p+1}),M(x_1,x_3,\dots ,x_{p+1}),\dots ,M(x_1,\dots ,x_p)\big )\\&\quad =K(x_1,\dots ,x_{p+1}), \text { for all }x_1,\dots ,x_{p+1} \in I \end{aligned}$$ K ( M ( x 2 , ⋯ , x p + 1 ) , M ( x 1 , x 3 , ⋯ , x p + 1 ) , ⋯ , M ( x 1 , ⋯ , x p ) ) = K ( x 1 , ⋯ , x p + 1 ) , for all x 1 , ⋯ , x p + 1 ∈ I in the family of means. Applying this procedure iteratively we can obtain a mean which is defined for vectors of arbitrary lengths starting from the bivariate one. The aim of this paper is to study the properties of such extensions.

Operator means and the reduced relative quantum entropy

We study operator means more general than the Kubo-Ando means. They are given as minima of geodesically convex functions and allow uniquely defined extensions to any number of variables. Multivariate hyper-means is a class of means of this type bounded from below by the arithmetic mean. We extend the definition of a hyper-man in the bivariate case and discover bivariate means that are not restrictions of the multivariate means studied earlier. We introduce the notion of reduced relative quantum entropy and prove that it is convex. The result is used to give a simplified proof of a theorem of Lieb and Seiringer.

Comparison of orders generated by Ky Fan type inequalities for bivariate means

In this paper, we deal with seven types of Ky Fan type relations between bivariate, symmetric and homogeneous means. For each relation we determine necessary and sufficient conditions for means to be in this relation. Additionally, we investigate the dependencies between these relations.

Sharp inequalities for Toader mean in terms of other bivariate means

In the paper, the author discovers the best constants $\alpha_1$, $\alpha_2$, $\alpha_3$, $\beta_1$, $\beta_2$ and $\beta_3$ for the double inequalities \[ \alpha_1 A\left(\frac{a-b}{a+b}\right)^{2n+2} < T(a,b)-\frac{1}{4}C-\frac{3}{4}A-A\sum_{k=1}^{n-1}\frac{(\frac{1}{2},k)^2}{4((k+1)!)^2}\left(\frac{a-b}{a+b}\right)^{2k+2}<\beta_1 A\left(\frac{a-b}{a+b}\right)^{2n+2} \] \[ \alpha_2 A\left(\frac{a-b}{a+b}\right)^{2n+2} < T(a,b)-\frac{3}{4}\overline{C}-\frac{1}{4}A-A\sum_{k=1}^{n-1}\frac{(\frac{1}{2},k)^2}{4((k+1)!)^2}\left(\frac{a-b}{a+b}\right)^{2k+2}<\beta_2 A\left(\frac{a-b}{a+b}\right)^{2n+2} \] and \[ \alpha_3 A\left(\frac{a-b}{a+b}\right)^{2n+2} < \frac{4}{5}T(a,b)+\frac{1}{5}H-A-A\sum_{k=1}^{n-1}\frac{(\frac{1}{2},k)^2}{5((k+1)!)^2}\left(\frac{a-b}{a+b}\right)^{2k+2}<\beta_3 A\left(\frac{a-b}{a+b}\right)^{2n+2} \] to be valid for all $a,b>0$ with $a\ne b$ and $n=1,2,\cdots$, where \[ C\equiv C(a,b)=\frac{a^2+b^2}{a+b},\,\overline{C}\equiv\overline{C}(a,b)=\frac{2(a^2+ab+b^2)}{3(a+b)},\, A\equiv A(a,b)=\frac{a+b}{2}, \] \[ H\equiv H(a,b) =\frac{2ab}{a+b},\quad T(a,b)=\frac2{\pi}\int_0^{\pi/2}\sqrt{a^2\cos^2\theta+b^2\sin^2\theta}\,{\rm d}\theta \] are respectively the contraharmonic, centroidal, arithmetic, harmonic and Toader means of two positive numbers $a$ and $b$, $ (a,n)=a(a+1)(a+2)(a+3)\cdots (a+n-1)$ denotes the shifted factorial function. As an application of the above inequalities, the author also find a new bounds for the complete elliptic integral of the second kind.

Some generalized Ostrowski type fractional integral inequalities for MT−convex functions with applications on special means

Some generalized Ostrowski-type integral inequalities for r−times differentiable functions whose absolute values are MT−convex have been discussed. Moreover, some applications on special bivariate means are obtained.

Objective Bayesian analysis of the ratio of bivariate lognormal means

In this study, we consider the objective Bayesian analysis for the ratio of means in the bivariate lognormal distribution, in which properly assigning priors for the ratio of means is challenging due to the presence of nuisance parameters. As a result, we create probability matching priors and reference priors for the ratio of means. Jeffreys’ prior and the two group reference prior do not satisfy a first-order matching criterion. We also investigate the posterior distribution property for the general prior class, which includes Jeffreys’ prior, the reference prior, and the matching prior. Through a simulation study, we check the frequentist coverage probabilities and compare them with the generalized confidence interval method. It demonstrated that the proposed probability matching priors match very well with the target coverage probabilities even when the sample sizes are small in a frequentist sense. Two real examples are also provided.

On a metric topology on the set of bivariate means

Abstract In this paper, we define a distance d on the set ℳ of bivariate means. We show that (ℳ, d) is a bounded complete metric space which is not compact. Other algebraic and topological properties of (ℳ, d) are investigated as well.

Sharp inequalities for the Toader mean of order -1 in terms of other bivariate means

Sharp inequalities for the Toader mean of order -1 in terms of other bivariate means

Further mean inequalities via some integral inequalities

Recently intensive efforts are deployed to establish inequalities involving some bivariate means. In this paper we aim to investigate further mean inequalities. The approach employed here is based on a combination of the integral representations of the involved means with some advanced integral inequalities known in the literature. In particular, applying the Gr?ss inequality and the Ostrowski inequality we derive a lot of estimations for differences between some standard means and weighted means.

Pelaksanaan Fungsi Manajemen Dan Kondisi Kerja Berhubungan Dengan Kepuasan Kerja Perawat

Kepuasan kerja merupakan bagian dari pengintegrasian sumber daya manusia, menjadi salah satu respon emosional aatas pekerjaan yag telah dilakukan. Tujuan penelitian ini untuk menganalisa hubugan antara elakanaan fungsi manajemen, kondisi kerja dan kepuasan kerja perawat di ruang rawat ina rumah sakit daerah kota Baubau. Jenis penelitian ini merupakan penelitian kuatitatif dengan pendekatan cross sectional study. Sampel dalam penelitian ini adalah 153 perawat yang bekerja diruang rawat inap, yang di peroleh degan menggunakan teknik total sampling. Pengumpulan data menggunakan kuesioner dengan skala likert. Analisa data univariat menggunakan tabel frekuensi dan analisa bivariat menggunakan uji spearman. Hasil enelitian menunjukan ada hubungan antara fungsi manajemen dan kepuasan kerja (p=0,001) dan ada hubungan antara kondisi kerja dan kepuasan kerja (p=0,036). Fungsi manjemen dan kondisi kerja berhubugan dega kepuasan kerja perawat. hasil penelitian dapat menjadi pertimbangan bagi rumah sakit pada umumnya dan manajemen rumah sakit perlu memperhatikan kondisi kerja perawat dan fungsi manajemen sehingga dapat menjaga kepuasan kerja perawat

Some new Simpson-type inequalities for generalized p-convex function on fractal sets with applications

The present article addresses the concept of p-convex functions on fractal sets. We are able to prove a novel auxiliary result. In the application aspect, the fidelity of the local fractional is used to establish the generalization of Simpson-type inequalities for the class of functions whose local fractional derivatives in absolute values at certain powers are p-convex. The method we present is an alternative in showing the classical variants associated with generalized p-convex functions. Some parts of our results cover the classical convex functions and classical harmonically convex functions. Some novel applications in random variables, cumulative distribution functions and generalized bivariate means are obtained to ensure the correctness of the present results. The present approach is efficient, reliable, and it can be used as an alternative to establishing new solutions for different types of fractals in computer graphics.

Penalized Fieller's confidence interval for the ratio of bivariate normal means.

Constructing a confidence interval for the ratio of bivariate normal means is a classical problem in statistics. Several methods have been proposed in the literature. The Fieller method is known as an exact method, but can produce an unbounded confidence interval if the denominator of the ratio is not significantly deviated from 0; while the delta and some numeric methods are all bounded, they are only first-order correct. Motivated by a real-world problem, we propose the penalized Fieller method, which employs the same principle as the Fieller method, but adopts a penalized likelihood approach to estimate the denominator. The proposed method has a simple closed form, and can always produce a bounded confidence interval by selecting a suitable penalty parameter. Moreover, the new method is shown to be second-order correct under the bivariate normality assumption, that is, its coverage probability will converge to the nominal level faster than other bounded methods. Simulation results show that our proposed method generally outperforms the existing methods in terms of controlling the coverage probability and the confidence width and is particularly useful when the denominator does not have adequate power to reject being 0. Finally, we apply the proposed approach to the interval estimation of the median response dose in pharmacology studies to show its practicalusefulness.

Estimates of quantum bounds pertaining to new q-integral identity with applications

In this article, we establish a new generalized q-integral identity involving a q-differentiable function. Using this new auxiliary result, we obtain some new associated quantum bounds essentially using the class of preinvex functions. At the end, we present some applications to the special bivariate means to show the significance of the obtained results. Our approaches and obtained results may lead to further applications in physics.

Some New Hermite–Hadamard-Type Inequalities Associated with Conformable Fractional Integrals and Their Applications

In this article, we establish some new Hermite–Hadamard-type inequalities involving the conformable fractional integrals. As applications, several inequalities for the approximation error in the midpoint formula and certain bivariate means are derived.

Abstract TP419: Medication Adherence as a Modulator of Ischemic Stroke Recurrence in the Veteran Population - The MISTER-VA Study

Introduction: Recurrent strokes make up 25% of the annual stroke incidence with 10% of the Veteran population suffering a recurrent stroke within 1 year. The role of adherence to a post-stroke medication regimen and its effect on stroke recurrence is unknown. Methods: Veterans evaluated in a vascular neurology specialty clinic from July 2010 to June 2016 underwent a detailed medical chart review and assessment of medication adherence to stroke prevention medications including anti-thrombotic use, anti-coagulants, anti-hypertensives, lipid-lowering therapy, and anti-hyperglycemic therapy. Medication adherence was measured by 90d refill history with >75% medication possession ratio (MPR) indicating adherence. A Framingham Stroke Risk Profile (FSRP) Score was calculated for each patient. Relative risk calculations were generated using a bivariate analysis and means compared via t-test. Results: 162 of 245 patients who were newly referred to the clinic underwent a detailed chart review and medication adherence profile. In this cohort, 93.8% were male and ranged in age between 35-94 years old (mean 69.2±10.2). The mean age of first stroke was 62.9±10.5 and the frequency of recurrent stroke was 26.5% (43 patients). The median time to recurrent stroke was 2.59 years. The average FSRP score for all subjects was 0.087±0.09 and did not differ between those with or without a recurrent stroke (0.103 vs. 0.082, p= 0.18). The rate of medication adherence in all subjects was 69.8% and differed greatly between those without and with a recurrent stroke, 79.0% vs. 44.2%, respectively. Median time to recurrent stroke was 2.59 years in those with MPR >75% and 1.91 years in those with MPR <75%. Strict adherence with a stroke prevention medication regimen was associated with a lower risk of recurrent stroke (relative risk = 0.34, 95% CI 0.21-0.57, p -value <0.0001) while poor adherence, was associated with a 2.91-fold increased risk ( p -value <0.0001) of recurrent stroke in the Veteran population. Conclusion: In this high-risk Veteran population, strict adherence with a stroke prevention medication regimen is associated with a lower risk of recurrent stroke. Efforts to measure and encourage medication adherence in patients with prior stroke may reduce the risk of recurrence.

Inequalities Involving Conformable Approach for Exponentially Convex Functions and Their Applications

In the article, we present several Hermite–Hadamard-type inequalities for the exponentially convex functions via conformable integrals. As applications, we give new inequalities for certain bivariate means.

Approximation for the complete elliptic integral of the first kind

In the article, we present several sharp upper and lower bounds for the complete elliptic integral of the first kind in terms of inverse trigonometric and inverse hyperbolic functions. As consequences, some sharp bounds for the Gaussian arithmetic-geometric mean in terms of other bivariate means are also given.

About a function that allows calculation of all symmetric homogeneous bivariate means

About a function that allows calculation of all symmetric homogeneous bivariate means

Hermite-Hadamard Type Inequalities via the Montgomery Identity

The main aim of this manuscript is to prove the result for Hermite-Hadamard types inequalities and to strengthen our results by giving applications for means. The proof of the result is based on the Montgomery identity. We use the Montgomery identity to establish a new identity regarding the Hermite-Hadamard inequality. Based on this identity with a class of convex and monotone functions and Jensen’s inequality, we obtain various results for the inequality. At the end, we also present applications for special bivariate means.

On Approximating the Toader Mean by Other Bivariate Means

In the article, we provide several sharp bounds for the Toader mean by use of certain combinations of the arithmetic, quadratic, contraharmonic, and Gaussian arithmetic-geometric means.