Optimal inequalities for the convex combination of error function
نویسندگان
چکیده
منابع مشابه
Optimal Inequalities for the Convex Combination of Error Function
For λ ∈ (0,1) and x,y > 0 we obtain the best possible constants p and r , such that erf(Mp(x,y;λ)) λ erf(x)+(1−λ) erf(y) erf(Mr(x,y;λ)) where erf(x) = 2 √π ∫ x 0 e −tdt and Mp(x,y;λ) = (λxp + (1− λ)yp)1/p(p = 0) , M0(x,y;λ) = xλ y1−λ are error function and weighted power mean, respectively. Furthermore, using these results, we generalized and complement an inequality due to Alzer.
متن کاملA Pair of Optimal Inequalities Related to the Error Function
The function V (x) ≡ √ πe x 2 [1 − erf(x)] (1) = ∞ 0 e −u √ x 2 + u du = 2e x 2 ∞ x e −t 2 dt arises in many contexts, from probability to mathematical physics, and satisi-fies the differential equation V ′ (x) = 2xV (x) − 2 with V (0) = √ π. (2) In this note, we restrict attention to x ≥ 0, in which case 0 < V (x) < 1/x and V (x) is decreasing. For x ≥ 0 we show that g π (x) ≤ V (x) < g 4 (x) (3)
متن کاملInequalities of Ando's Type for $n$-convex Functions
By utilizing different scalar equalities obtained via Hermite's interpolating polynomial, we will obtain lower and upper bounds for the difference in Ando's inequality and in the Edmundson-Lah-Ribariv c inequality for solidarities that hold for a class of $n$-convex functions. As an application, main results are applied to some operator means and relative operator entropy.
متن کاملOptimal convex error estimators for classification
A cross-validation error estimator is obtained by repeatedly leaving out some data points, deriving classifiers on the remaining points, computing errors for these classifiers on the left-out points, and then averaging these errors. The 0.632 bootstrap estimator is obtained by averaging the errors of classifiers designed from points drawn with replacement and then taking a convex combination of...
متن کاملextensions of some polynomial inequalities to the polar derivative
توسیع تعدادی از نامساوی های چند جمله ای در مشتق قطبی
15 صفحه اولذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Inequalities
سال: 2015
ISSN: 1846-579X
DOI: 10.7153/jmi-09-08