Rocky Mountain Journal of Mathematics

A differential inequality and starlikeness of a double integral

Sarika Verma, Sushma Gupta, and Sukhjit Singh

Full-text: Open access

Abstract

The main objective of this paper is to discuss starlikeness of order $\beta$ of the solutions of a differential equation and, as a consequence, to obtain conditions on the kernel function $g$ such that the function defined by \[ f(z)=\int_0^1 \int_0^1 g(r,s,z)\,dr\,ds \] is a starlike function of the same order.

Article information

Source
Rocky Mountain J. Math., Volume 44, Number 5 (2014), 1653-1659.

Dates
First available in Project Euclid: 1 January 2015

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1420071559

Digital Object Identifier
doi:10.1216/RMJ-2014-44-5-1653

Mathematical Reviews number (MathSciNet)
MR3295647

Zentralblatt MATH identifier
1303.30018

Subjects
Primary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
Secondary: 30C80: Maximum principle; Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination

Keywords
Differential sub ordination starlike function convex function

Citation

Verma, Sarika; Gupta, Sushma; Singh, Sukhjit. A differential inequality and starlikeness of a double integral. Rocky Mountain J. Math. 44 (2014), no. 5, 1653--1659. doi:10.1216/RMJ-2014-44-5-1653. https://projecteuclid.org/euclid.rmjm/1420071559


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References

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