SCHUR-GEOMETRIC CONVEXITY OF STOLARSKY'S EXTENDED MEAN VALUES
نویسندگان
چکیده
منابع مشابه
Necessary and Sufficient Conditions for the Schur Harmonic Convexity or Concavity of the Extended Mean Values
In this paper, we prove that the extended values E(r, s;x, y) are Schur harmonic convex (or concave, respectively) with respect to (x, y) ∈ (0,∞) × (0,∞) if and only if (r, s) ∈ {(r, s) : s ≥ −1, s ≥ r, s+ r + 3 ≥ 0} ∪ {(r, s) : r ≥ −1, r ≥ s, s+r+3 ≥ 0} (or {(r, s) : s ≤ −1, r ≤ −1, s+r+3 ≤ 0}, respectively).
متن کاملSchur-convexity, Schur-geometric and Schur-harmonic convexity for a composite function of complete symmetric function
In this paper, using the properties of Schur-convex function, Schur-geometrically convex function and Schur-harmonically convex function, we provide much simpler proofs of the Schur-convexity, Schur-geometric convexity and Schur-harmonic convexity for a composite function of the complete symmetric function.
متن کاملResearch Article Schur-Convexity of Two Types of One-Parameter Mean Values in n Variables
and let dμ= du1, . . . ,dun−1 be the differential of the volume in En−1. The weighted arithmetic mean A(x,u) and the power mean Mr(x,u) of order r with respect to the numbers x1,x2, . . . ,xn and the positive weights u1,u2, . . . ,un with ∑n i=1ui = 1 are defined, respectively, as A(x,u) = ∑ni=1uixi, Mr(x,u) = (∑ni=1uixr i ) for r =0, and M0(x,u)= ∏n i=1x ui i . For u=(1/n,1/n, . . . ,1/n), we ...
متن کاملSchur convexity of the generalized geometric Bonferroni mean and the relevant inequalities
In this paper, we discuss the Schur convexity, Schur geometric convexity and Schur harmonic convexity of the generalized geometric Bonferroni mean. Some inequalities related to the generalized geometric Bonferroni mean are established to illustrate the applications of the obtained results.
متن کاملSchur–convexity, Schur Geometric and Schur Harmonic Convexities of Dual Form of a Class Symmetric Functions
By the properties of Schur-convex function, Schur geometrically convex function and Schur harmonically convex function, Schur-convexity, Schur geometric and Schur harmonic convexities of the dual form for a class of symmetric functions are simply proved. As an application, several inequalities are obtained, some of which extend the known ones. Mathematics subject classification (2010): 26D15, 0...
متن کاملذخیره 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: International Journal of Pure and Apllied Mathematics
سال: 2017
ISSN: 1311-8080,1314-3395
DOI: 10.12732/ijpam.v114i1.7