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


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

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

First available in Project Euclid: 1 January 2015

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Differential sub ordination starlike function convex function


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.

Export citation


  • R. Fournier and P.T. Mocanu, Differential inequalities and starlikeness, Complex Var. Theor. Appl. 48 (2003), 283–292.
  • S.S. Miller and P.T. Mocanu, Differential subordinations–Theory and applications, Marcel Dekker, New York, 1999.
  • M. Obradovic, Simple sufficient conditions for univalence, Mat. Vesn. 49 (1997), 241–244.