Log-concavity for Bernstein-type operators using stochastic orders

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:413

Article

Badia, F. G.¹  Sangueesa, C.¹ 

[1] Univ Zaragoza, Dept Metodos Estadist, Zaragoza, Spain

关键词: Log-concavity;    Bernstein-type operator;    Szasz operator;    Gamma operator;    Stochastic order;    Incomplete Gamma function;   

DOI  :  10.1016/j.jmaa.2013.12.014

来源: Elsevier

【 摘 要 】

This paper aims to study the preservation of log-concavity for Bernstein-type operators. In particular, attention is focused on positive linear operators, defined on the positive semi-axis, admitting a probabilistic representation in terms of a process with independent increments. This class includes the classical Gamma, Szasz, and Szasz-Durrmeyer operators. With respect to the first and second operators, the results of this paper correct two erroneous counterexamples in [10]. As a main tool in our results we use stochastic order techniques. Our results include, as a particular case, the log-concavity of certain functions related to the incomplete Gamma function. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free