Optimal lower and upper bounds for the geometric convex combination of the 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 کاملUpper and lower bounds for numerical radii of block shifts
For an n-by-n complex matrix A in a block form with the (possibly) nonzero blocks only on the diagonal above the main one, we consider two other matrices whose nonzero entries are along the diagonal above the main one and consist of the norms or minimum moduli of the diagonal blocks of A. In this paper, we obtain two inequalities relating the numeical radii of these matrices and also determine ...
متن کاملThe Optimal Upper and Lower Power Mean Bounds for a Convex Combination of the Arithmetic and Logarithmic Means
and Applied Analysis 3 Lemma 2.1. If α ∈ 0, 1 , then 1 2α log 2 − logα > 3 log 2. Proof. For α ∈ 0, 1 , let f α 1 2α log 2 − logα , then simple computations lead to f ′ α 2 ( log 2 − 1 − 2 logα − 1 α , 2.1 f ′′ α 1 α2 1 − 2α . 2.2 From 2.2 we clearly see that f ′′ α > 0 for α ∈ 0, 1/2 , and f ′′ α < 0 for α ∈ 1/2, 1 . Then from 2.1 we get f ′ α ≤ f ′ ( 1 2 ) 4 ( log 2 − 1 < 0 2.3 for α ∈ 0, 1 ....
متن کاملOptimal Convex Combination Bounds of Seiffert and Geometric Means for the Arithmetic Mean
We find the greatest value α and the least value β such that the double inequality αT (a,b) + (1−α)G(a,b) < A(a,b) < βT (a,b) + (1− β)G(a,b) holds for all a,b > 0 with a = b . Here T (a,b) , G(a,b) , and A(a,b) denote the Seiffert, geometric, and arithmetic means of two positive numbers a and b , respectively. Mathematics subject classification (2010): 26E60.
متن کاملinvestigating the feasibility of a proposed model for geometric design of deployable arch structures
deployable scissor type structures are composed of the so-called scissor-like elements (sles), which are connected to each other at an intermediate point through a pivotal connection and allow them to be folded into a compact bundle for storage or transport. several sles are connected to each other in order to form units with regular polygonal plan views. the sides and radii of the polygons are...
ذخیره 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 Inequalities and Applications
سال: 2015
ISSN: 1029-242X
DOI: 10.1186/s13660-015-0906-y