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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...
Sufficient Conditions for Starlikeness and Convexity in $|z|< 1/2$
Analytic Starlike Convex
2010/1/22
For analytic functions with in the open unit disc , T. H. MacGregor has considered some conditions for to be starlike or convex. The object of the present paper is to discuss some interesting probl...
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...
A Note on Quasiconvexity and Rank-one Convexity for 2$\times$2 Matrices
Quasiconvexity 2$\times$2 Matrices Rank-one Convexity
2009/1/22
We report on an attempt to find a counterexample to the statement that rank-one convexity does not imply quasiconvexity in the case of 2$\times$2 matrices. The failure of such attempt is a consequence...
Total Convexity for Powers of the Norm in Uniformly Convex Banach Spaces
Uniformly Convex Banach Spaces Norm Total Convexity
2009/1/13
The aim of the paper is to show that, in uniformly convex Banach spaces, the powers of the norm with exponent r > 1 share a property called total convexity. Using this fact we establish a formula for ...
A Note on the Modulus of $U$-Convexity and Modulus of $W^*$-Convexity
Modulus of U-convexity Modulus of W*-convexity Coefficient of weak orthogonality Uniform normal
2010/1/25
We present some sufficient conditions for which a Banach space has normal structure in term of the modulus of -convexity, modulus of -convexity and the coefficient of weak orthogonality. Some known r...
On Starlikeness and Convexity of Analytic Functions Satisfying a Differential Inequality
Multivalent function Starlike function Convex function Multiplier transformation
2010/1/22
In the present paper, the authors investigate a differential inequality defined by multiplier transformation in the open unit disk E = {z:|z|
$S$-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.