On a Univalent Class Involving Differential Subordinations with Applications
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.
DOI: https://doi.org/10.3844/jmssp.2011.137.143
Copyright: © 2011 R. W. Ibrahim and M. Darus. This is an open access article distributed under the terms of the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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Keywords
- Convex functions
- close-to-convex functions
- differential subordination
- superordination
- unit disk
- sandwich theorem
- hadamard product
- dziok-srivastava linear operator
- differential sandwich