The convexity of the integral operator on the class of $B(\mu,\alpha)$

Stanciu, L.; Breaz, D.

doi:10.22075/ijnaa.2012.41

The convexity of the integral operator on the class of $B (μ, α)$

Document Type : Research Paper

Authors

L. Stanciu ¹
D. Breaz ²

¹ Department of Mathematics, Targul din Vale Str., No.1, 110040, Pitesti, Arges, Romania

² Department of Mathematics, Alba Iulia, Str. N. Iorga, 510000, No. 11-13, Romania

10.22075/ijnaa.2012.41

Abstract

In this paper, we study the convexity of the integral operator $\int_{0}^{z} \prod_{i = 1}^{n} (t e^{f_{i} (t)})^{γ_{i}} d t$ where the function $f_{i}, i \in {1, 2, \dots, n}$ satisfy the condition
$| f_{i}^{'} (z) (\frac{z}{f_{i} (z)})^{μ_{i}} - 1 | < 1 - α_{i}, i \in {1, 2, \dots, n} .$