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

Document Type : Research Paper


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


In this paper, we study the convexity of the integral operator $\int_0^z\prod_{i=1}^n(te^{f_i(t)})^{\gamma_i}dt$  where the function $f_i, i\in\{1,2,\ldots,n\}$  satisfy the condition
$$|f_i'(z)(\frac{z}{f_i(z)})^{\mu_i}-1|<1-\alpha_i,\quad i\in\{1,2,\ldots,n\}.$$


  • Receive Date: 03 October 2011
  • Revise Date: 03 November 2011
  • Accept Date: 03 August 2012
  • First Publish Date: 03 August 2012