New general integral operator

For αi,βiαi,βi positive real numbers for all i=1,…,ni=1,…,n, we introduce a new integral operator of analytic functions Iαi,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)N(δ). Furthermore, we determine the order of convexity of Iαi,βi(f1,…,fn)(z).