- Research Article
- Open Access
A New General Integral Operator Defined by Al-Oboudi Differential Operator
© Serap Bulut. 2009
- Received: 8 December 2008
- Accepted: 22 January 2009
- Published: 28 January 2009
We define a new general integral operator using Al-Oboudi differential operator. Also we introduce new subclasses of analytic functions. Our results generalize the results of Breaz, Güney, and Sălăgean.
- Analytic Function
- Differential Operator
- Convex Function
- Integral Operator
- Geometric Interpretation
When , we get Sălăgean's differential operator .
From elementary computations we see that represents the conic sections symmetric about the real axis. Thus is an elliptic domain for , a parabolic domain for , a hyperbolic domain for and a right-half plane for .
- D.Breaz and N. Breaz  introduced and studied the integral operator
The following lemma will be required in our investigation.
which is the desired result.
From Corollary 2.3, we immediately get Corollary 2.4.
If we set in Corollary 2.4, then we have [7, Theorem 1]. So Corollary 2.4 is an extension of Theorem 1.
Corollary 2.8 readily follows from Corollary 2.7.
If we set in Corollary 2.8, then we have [7, Corollary 1].
The proof is similar to the proof of Theorem 2.2.
If we set in Corollary 2.11, then we have [7, Theorem 2].
If we set in Corollary 2.14, then we have [7, Corollary 2].
If we set in Corollary 2.17, then we have [7, Theorem 3].
If we set in Corollary 2.20, then we have [7, Theorem 4].
If we set in Corollary 2.23, then we have [7, Theorem 5].
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