Research Article Open Access

On a Univalent Class Involving Differential Subordinations with Applications

R. W. Ibrahim and M. Darus

Abstract

Problem statement: By means of the Hadamard product (or convolution), new class of analytic functions was formed. This class was motivated by many authors. Approach: By using the concept of the subordination and superordination, we define certain differential inequalities and first order differential subordinations. Results: As their applications, we obtain some sufficient conditions for univalence which generalize and refine some previous results. Sandwich theorem is also obtained. Conclusion: Therefore, we posed a new class of analytic functions which generalized some well known subclasses. This class involves the E(Φ,ψ) - family of functions.

Journal of Mathematics and Statistics
Volume 7 No. 2, 2011, 137-143

DOI: https://doi.org/10.3844/jmssp.2011.137.143

Submitted On: 23 September 2010 Published On: 18 May 2011

How to Cite: Ibrahim, R. W. & Darus, M. (2011). On a Univalent Class Involving Differential Subordinations with Applications. Journal of Mathematics and Statistics, 7(2), 137-143. https://doi.org/10.3844/jmssp.2011.137.143

  • 3,423 Views
  • 1,918 Downloads
  • 1 Citations

Download

Keywords

  • Convex functions
  • close-to-convex functions
  • differential subordination
  • superordination
  • unit disk
  • sandwich theorem
  • hadamard product
  • dziok-srivastava linear operator
  • differential sandwich