2007/01/09 by G. D. Anderson, M. K. Vamanamurthy, Матти Вуоринен +1 · 1 citation
Mathematics · #Analytic and geometric function theory #Bessel function #Combinatorics #Convex function #Convexity #Function (biology) #Functional Equations Stability Results #Generalized hypergeometric function #Geometry #Harmonic mean #Hypergeometric function #Mathematical Inequalities and Applications #Mathematical analysis #Mathematics #Pure mathematics #Regular polygon #Series (stratigraphy) #Statistics #math.CA #msc:26A51 #msc:33C05 #msc:33C20
paper · pdf · doi:10.1016/j.jmaa.2007.02.016
published as J. Math. Anal. Appl. 335 (2007), 1294-1308 · 17 pages
arxiv created 2007/01/09 · openalex publication_date 2007/02/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Let R+ = (0,infinity) 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 in M, we say that a function f : R+ to R+ is (m1,m2)-convex if f(m1(x,y)) < or = m2(f(x),f(y)) for all x, y in R+ . The usual convexity is the special case when both mean values are arithmetic means. We study the dependence of (m1,m2)-convexity on m1 and m2 and give sufficient conditions for (m1,m2)-convexity of functions defined by Maclaurin series. The criteria involve the Maclaurin coefficients. Our results yield a class of new inequalities for several special functions such as the Gaussian hypergeometric function and a generalized Bessel function.