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The 2-log-convexity of the Apéry Numbers
Apery numbers log-convexity 2-log-convexity infinite log-convexity
2014/6/3
We present an approach to proving the 2-log-convexity of sequences satisfying three-term recurrence relations. We show that the Apéry numbers, the Cohen-Rhin numbers, the Motzkin numbers, the Fine num...
A note on convexity and starshapedness
Convex sets wn-convex sets starshaped sets affine sets
2010/11/1
We establish sufficient and necessary conditions for a set to be affine or convex. The concepts of weak near convexity and affine starshapedness are studied. A characterization of the (affine) kernel ...
Schur Positivity and the q-Log-convexity of the Narayana Polynomials
q-log-concavity q-log-convexity q-Narayana number Narayana polynomial lattice permutation Schur positivity Littlewood-Richardson rule
2014/6/3
Using Schur positivity and the principal specialization of Schur functions, we provide a proof of a recent conjecture of Liu and Wang on the q-log-convexity of the Narayana polynomials, and a proof of...
The q-log-convexity of the Narayana polynomials of type B
q-log-convexity Schur positivity Pieri's rule the Jacobi-Trudi identity principal specialization Narayana numbers of type B
2014/6/3
We prove a conjecture of Liu and Wang on the q-log-convexity of the Narayana polynomials of type B. By using Pieri's rule and the Jacobi-Trudi identity for Schur functions, we obtain an expansion of a...
Generalized convexity and invexity in optimization theory: Some new results
Generalized convexity and invexity optimization theory
2010/9/15
Convex like properties, without vector space structure are intensively used in the minimax theory Since Ky Fan has proved the first minimax theorem for concave-convexlike functions, several authors ha...
$S$-Geometric Convexity of a Function Involving Maclaurin's Elementary Symmetric Mean
Geometrically convex function $S$-geometrically convex function Inequality Maclaurin-Inequality
2008/7/3
$S$-Geometric Convexity of a Function Involving Maclaurin's Elementary Symmetric Mean.
Convexity of the Zero-Balanced Gaussian Hypergeometric Functions with Respect to H鰈der Means
Multiplicatively convexity Log-convexity Hypergeometric functions Hö lder means
2008/7/1
In this note we investigate the convexity of zero-balanced Gaussian hypergeometric functions and general power series with respect to Hölder means.
Convexity of Weighted Stolarsky Means.
Improved $GA$- Convexity Inequalities
Convex functions $GA$-convexity Symmetric functions IMO competition
2008/7/1
We consider a class of algebraic inequalities for functions of n variables depending on parameters that generalise the case of GA-convex functions. The functions in this class are GA-convex only in a ...
Improvements of Euler-Trapezoidal Type Inequalities with Higher-Order Convexity and Applications
Hadamard inequality Euler formula Convex functions Integral inequalities Numerical integration
2008/7/1
We improve a bounds relating to Euler's formula for the case of a function with higher-order convexity properties. These are used to improve estimates of the error involved in the use of the trapezoid...
Geometric Convexity of a Function Involving Gamma Function and Applications to Inequality Theory
Gamma function Geometrically Convex function Wallis' inequality Application Inequality
2008/7/1
In this paper, the geometric convexity of a function involving gamma function is studied, as applications to inequality theory, some important inequalities which improve some known inequalities, inclu...
Ky Fan's Inequality via Convexity.
Monotonicity and Convexity for the Gamma Function.
On a Generalization of Alpha Convexity
Starlike Convex Strongly alpha-convex Bounded boundary rotation
2008/6/30
On a Generalization of Alpha Convexity.
Monotonicity and Convexity of Four Sequences Originating from Nanson's Inequality
Monotonicity Convexity Sequence Nanson's inequality Refinement
2008/6/30
In the short note, four sequences originating from Nanson's inequality are introduced, their monotonicities and convexities are obtained, and Nanson's inequality is refined.