Univalency Conditions of A General Nonlinear Analytic Integral Operator with Different Domains

By using the subordination relationship and the sufficient conditions of univalent functions, some generalized nonlinear analytic integral operators J_n, \sigma\left(\mathfrakA_n, \mathfrakB_n\right)(z) are researched, and the sufficient conditions for the analytic integral operator to be univalent in different regions are obtained. The sufficiency of the relevant nonlinear analytic integral operator to be univalent are generalized. The sufficient conditions for integral operators to be univalent in a strip region are derived.