Taiwanese Journal of Mathematics

Some Sufficient Conditions for Univalence of Certain Families of Integral Operators Involving Generalized Bessel Functions

Erhan Erhan, Halit Orhan, and H. M. Srivastava

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Abstract

The main object of this paper is to give sufficient conditions for certain families of integral operators, which are defined here by means of the normalized form of the generalized Bessel functions, to be univalent in the open unit disk. In particular cases, we find the corresponding simpler conditions for integral operators involving the Bessel function, the modified Bessel function and the spherical Bessel function.

Article information

Source
Taiwanese J. Math., Volume 15, Number 2 (2011), 883-917.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406240

Digital Object Identifier
doi:10.11650/twjm/1500406240

Mathematical Reviews number (MathSciNet)
MR2810187

Zentralblatt MATH identifier
1242.30011

Subjects
Primary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.) 33C10: Bessel and Airy functions, cylinder functions, $_0F_1$
Secondary: 30C20: Conformal mappings of special domains 30C75: Extremal problems for conformal and quasiconformal mappings, other methods

Keywords
analytic functions open unit disk univalent functions univalence conditions integral operators generalized Bessel functions Bessel modified Bessel and spherical Bessel functions Ahlfors-Becker and Becker univalence criteria Schwarz lemma

Citation

Erhan, Erhan; Orhan, Halit; Srivastava, H. M. Some Sufficient Conditions for Univalence of Certain Families of Integral Operators Involving Generalized Bessel Functions. Taiwanese J. Math. 15 (2011), no. 2, 883--917. doi:10.11650/twjm/1500406240. https://projecteuclid.org/euclid.twjm/1500406240


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