NEW RESULTS RELATED TO THE CONVEXITY OF THE BERNARDI INTEGRAL OPERATOR

作者：Oros Georgia Irina^*

来源：Journal of Mathematical Inequalities, 2013, 7(3): 535-541.

DOI：10.7153/jmi-07-49

• Analytic function
• univalent function
• integral operator
• convex function
• close-to-convex function

In this paper we prove the convexity of the image of a close-to-convex function by the Bernardi integral operator given by
L-gamma(f)(z) = F(z) = gamma+1/z(gamma) integral(z)(0) f(t)t(gamma-1)dt, z is an element of U. (1)
This result extends the result obtained by N. Pascu in [9], where it has been shown that the Bernardi operator transforms a close-to-convex function into a close-to-convex function under certain conditions.

• 出版日期2013-9