Certain Bounds for the Differences of Means
نویسندگان
چکیده
Let Pn,r(x) be the generalized weighted power means. We consider bounds for the differences of means in the following form: max { Cu,v,β x 1 , Cu,v,β x n } σn,w′,β ≥ P n,u − P n,v α ≥ min { Cu,v,β x 1 , Cu,v,β x n } σn,w,β . Here β 6= 0, σn,t,β( x) = ∑n i=1 ωi[x β i −P β n,t(x)] andCu,v,β = u−v 2β2 . Some similar inequalities are also considered. The results are applied to inequalities of Ky Fan’s type.
منابع مشابه
Optimal convex combinations bounds of centrodial and harmonic means for logarithmic and identric means
We find the greatest values $alpha_{1} $ and $alpha_{2} $, and the least values $beta_{1} $ and $beta_{2} $ such that the inequalities $alpha_{1} C(a,b)+(1-alpha_{1} )H(a,b)
متن کاملStability for certain subclasses of harmonic univalent functions
In this paper, the problem of stability for certain subclasses of harmonic univalent functions is investigated. Some lower bounds for the radius of stability of these subclasses are found.
متن کاملUPPER BOUNDS FOR FINITENESS OF GENERALIZED LOCAL COHOMOLOGY MODULES
Let $R$ be a commutative Noetherian ring with non-zero identity and $fa$ an ideal of $R$. Let $M$ be a finite $R$--module of finite projective dimension and $N$ an arbitrary finite $R$--module. We characterize the membership of the generalized local cohomology modules $lc^{i}_{fa}(M,N)$ in certain Serre subcategories of the category of modules from upper bounds. We define and study the properti...
متن کاملKy Fan Inequality and Bounds for Differences of Means
We prove an equivalent relation between Ky Fan-type inequalities and certain bounds for the differences of means. We also generalize a result of Alzer et al. 1. Introduction. Let P n,r (x) be the generalized weighted power means: P n,r (x) = (n i=1 ω i x
متن کاملOn a linear combination of classes of harmonic $p-$valent functions defined by certain modified operator
In this paper we obtain coefficient characterization, extreme points and distortion bounds for the classes of harmonic $p-$valent functions defined by certain modified operator. Some of our results improve and generalize previously known results.
متن کاملCertain Inequalities for a General Class of Analytic and Bi-univalent Functions
In this work, the subclass of the function class S of analytic and bi-univalent functions is defined and studied in the open unit disc. Estimates for initial coefficients of Taylor- Maclaurin series of bi-univalent functions belonging these class are obtained. By choosing the special values for parameters and functions it is shown that the class reduces to several earlier known classes of analy...
متن کامل