Radii of starlikeness and convexity of some q-Bessel functions

Autor(es)

Baricz, Arpad ^{[1, 2]} ; Dimitrov, Dimitar K. ^[3] ; Mezo, Istvan ^[4]

Afiliação do(s) autor(es)

^[1] Univ Babes Bolyai, Dept Econ, Cluj Napoca 400591 - Romania

^[2] Obuda Univ, Inst Appl Math, H-1034 Budapest - Hungary

^[3] Univ Estadual Paulista UNESP, IBILCE, Dept Matemat Aplicada, BR-15054 Sao Jose Do Rio Preto - Brazil

^[4] Nanjing Univ Informat Sci & Technol, Dept Math, Nanjing, Jiangsu - Peoples R China

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Analysis and Applications; v. 435, n. 1, p. 968-985, MAR 1 2016.
• Citações Web of Science: 8

Resumo

Geometric properties of the Jackson and Hahn-Exton q-Bessel functions are studied. For each of them, three different normalizations are applied in such a way that the resulting functions are analytic in the unit disk of the complex plane. For each of the six functions we determine the radii of starlikeness and convexity precisely by using their Hadamard factorization. These are q-generalizations of some known results for Bessel functions of the first kind. The characterization of entire functions from the Laguerre-Polya class via hyperbolic polynomials plays an important role in this paper. Moreover, the interlacing property of the zeros of Jackson and Hahn-Exton q-Bessel functions and their derivatives is also useful in the proof of the main results. We also deduce a necessary and sufficient condition for the close-to-convexity of a normalized Jackson q-Bessel function and its derivatives. Some open problems are proposed at the end of the paper. (C) 2015 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 09/13832-9 - Polinômios ortogonais, funções especiais e aplicações
• Beneficiário: Dimitar Kolev Dimitrov
• Linha de fomento: Auxílio à Pesquisa - Temático