Well Behaved Asymptotical Convex Functions (original) (raw)

On the Asymptotically Well Behaved Functions and Global Error Bound for Convex Polynomials

SIAM Journal on Optimization, 2010

In this paper, we present some new and tractable sufficient conditions for convex asymptotic well behaved (AWB) functions. Moreover, we establish several Lipschitz/Hölder type global error bound results for single convex polynomial and for function which can be expressed as maximum of finitely many nonnegative convex polynomials. An advantage of our approach is that the corresponding Hölder exponent in our Hölder type global error bound results can be determined explicitly. .au † Sometimes, we also use x R m (in stead of x ), if the underlying space need to be specified

Uniformly convex and uniformly smooth convex functions

Annales de la faculté des sciences de Toulouse Mathématiques, 1995

Uniformly convex and uniformly smooth convex functions Annales de la faculté des sciences de Toulouse 6 e série, tome 4, n o 4 (1995), p. 705-730 http://www.numdam.org/item?id=AFST\_1995\_6\_4\_4\_705\_0 © Université Paul Sabatier, 1995, tous droits réservés. L'accès aux archives de la revue « Annales de la faculté des sciences de Toulouse » (http://picard.ups-tlse.fr/\~annales/) implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/-705

Some Remarks on Close-To-Convex and Strongly Convex Functions

Mathematica Scandinavica

We examine the boundedness of | arg{p(z)}| provided by the boundedness of |arg (1 + zp (z)/p(z))|, for some analytic function p. The paper determines the order of strongly close-to-convexity in the class of strongly convex functions. Also, we consider conditions that are sufficient for a function to be a Bazilevic function.

Estimation of a Convex Function: Charactenzatl<) fiS and Asymptotic Theory

2000

Abstract:" Ve study nonparametric estimation of convex regression and density functions methods of least squares (in the and density and maximum likelihood (in the density estimation.\ Ale provide characterizations of these estimators, prove that they are consistent, and establish their distributions at a fixed point of positive curvature of the functions estimated. The asymptotic distribution theory relies on the existence of a" invelope function" for integrated two-sided Brownian motion t4 which is established in the ...

Two Parameter Families of Close-To-Convex Functions and Convolution Theorems

Analysis, 2004

Using a recently obtained coefficient condition for functions with positive real part by M. Obradović and S. Ponnusamy, we construct four different useful examples of two parameter families of close-to-convex functions. As a consequence of another well-known coefficient condition due to M. Obradović and S. Ponnusamy, we obtain a number of results concerning the convolution of two univalent functions. Using these results, we obtain criteria for combinations of hypergeometric functions to be univalent.

On approximately convex functions

Proceedings of the American Mathematical Society, 1993

The Bernstein-Doetsch theorem on midconvex functions is extended to approximately midconvex functions and to approximately Wright convex functions.

Some subclasses of close-to-convex functions

Annales Polonici Mathematici

For α ∈ [0, 1] and β ∈ (−π/2, π/2) we introduce the classes C β (α) defined as follows: a function f regular in U = {z : |z| < 1} of the form f (z) = z + ∞ n=1 anz n , z ∈ U , belongs to the class C β (α) if Re{e iβ (1 − α 2 z 2)f (z)} > 0 for z ∈ U. Estimates of the coefficients, distortion theorems and other properties of functions in C β (α) are examined.

Almost approximately convex functions

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