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We determine the complete membership to Kaplan classes of a family of functions that can be presented in the form of integral operators  I1 ( f, g ;  α, β ) introduced by Kim and Merkes as well as  I2 ( f, g ;  α ) introduced by Ularu and Breaz. In this way we obtain close-to-convexity criteria for these functions.

Complete membership to Kaplan classes of a certain class of functions