On Inequalities for Hypergeometric Analogues of the Arithmetic-geometric Mean
نویسندگان
چکیده
In this note, we present sharp inequalities relating hypergeometric analogues of the arithmetic-geometric mean discussed in [5] and the power mean. The main result generalizes the corresponding sharp inequality for the arithmetic-geometric mean established in [10].
منابع مشابه
Some topological indices of graphs and some inequalities
Let G be a graph. In this paper, we study the eccentric connectivity index, the new version of the second Zagreb index and the forth geometric–arithmetic index.. The basic properties of these novel graph descriptors and some inequalities for them are established.
متن کاملm at h . C A ] 9 J an 2 00 7 GENERALIZED CONVEXITY AND INEQUALITIES
Let R+ = (0,∞) and let M be the family of all mean values of two numbers in R+ (some examples are the arithmetic, geometric, and harmonic means). Given m1, m2 ∈ M, we say that a function f : R+ → R+ is (m1, m2)-convex if f(m1(x, y)) ≤ m2(f(x), f(y)) for all x, y ∈ R+. The usual convexity is the special case when both mean values are arithmetic means. We study the dependence of (m1, m2)-convexit...
متن کاملA Note on the First Geometric-Arithmetic Index of Hexagonal Systems and Phenylenes
The first geometric-arithmetic index was introduced in the chemical theory as the summation of 2 du dv /(du dv ) overall edges of the graph, where du stand for the degree of the vertex u. In this paper we give the expressions for computing the first geometric-arithmetic index of hexagonal systems and phenylenes and present new method for describing hexagonal system by corresponding a simple g...
متن کاملSome remarks on the arithmetic-geometric index
Using an identity for effective resistances, we find a relationship between the arithmetic-geometric index and the global ciclicity index. Also, with the help of majorization, we find tight upper and lower bounds for the arithmetic-geometric index.
متن کاملOn Inequalities for 2F1 and Related Means
This informal working paper provides an expository survey of some inequalities and associated conjectures involving the Gaussian hypergeometric function 2F1 and closely related bivariate means. Recent as well as previously established results are presented for which the conjectures are known to hold. This basic investigation begins with the fundamental concept of a bivariate mean which is defin...
متن کامل