Inequalities involving certain integral operators. (English) Zbl 1161.30305

Aouf, M. K.

J. Math. Inequal. 2, No. 4, 537-547 (2008).

Summary: Two integral operators \(l^\alpha_p\) (\(\alpha>0\); \(p\in \mathbb N)\) and \(Q^\alpha_{\beta,p}\) \((\alpha>0; \beta>-1; p\in \mathbb N\), where \(\mathbb N=\{1,2,\ldots \}\), are introduced for functions of the form \(f(z)=\sum_{n=1}^\infty a_{p+n}z^{p+n}\) which are analytic and \(p\)-valent in the open unit disc \(U=\{z:| z|<1\}\). The object of the present paper is to give an application of the above operators to differential inequalities.

MSC:

30C45

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)

Keywords:

analytic function; \(p\)-valent function; integral operator