New general integral operator

Abstract

For αi,βi positive real numbers for all i=1,...,n, we introduce a new integral operator of analytic functions I αi,βi(f1,...,fn)(z) defined by Iαi,βi(f1,..., fn)(z)=∫0z∏i=1n(fi′(t))αi( fi(t)t)βidt. In this paper, we obtain sufficient conditions for this operator to be in the class N(δ). Furthermore, we determine the order of convexity of Iαi, βi(f1,...,fn)(z). © 2011 Elsevier Ltd. All rights reserved.