Some Applications of Srivastava-Attiya Operator to p-Valent Starlike Functions
© E. A. Elrifai et al. 2010
Received: 25 March 2010
Accepted: 14 July 2010
Published: 1 August 2010
We introduce and study some new subclasses of p-valent starlike, convex, close-to-convex, and quasi-convex functions defined by certain Srivastava-Attiya operator. Inclusion relations are established, and integral operator of functions in these subclasses is discussed.
When the operator is well-known Srivastava-Attiya operator .
In this paper, we will establish inclusion relation for these classes and investigate Srivastava-Attiya operator for these classes.
We note that
for being any negative integer, and , the operator was studied by S l gean .
2. Inclusion Relation
In order to prove our main results, we will require the following lemmas.
Lemma 2.1 (see ).
Lemma 2.2 (see ).
Our first inclusion theorem is stated as follows.
This completes the proof of Theorem 2.3.
which evidently proves Theorem 2.4.
The proof of Theorem 2.6 is complete.
3. Integral Operator
The proof of Theorem 3.1 is complete·
This completes the proof of Theorem 3.2.
and the proof of Theorem 3.4 is complete.
The authors would like to thank the referees of the paper for their helpful suggestions.
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