In this paper, the function classes 𝒮𝒫𝑝(𝜎,𝜈)SP�(�,�) and 𝒰𝒞𝒮𝒫(𝜎,𝜈)UCSP(�,�) are investigated for the normalized Wright functions. More precisely, several sufficient and necessary conditions are provided so that the aforementioned functions are in these classes. Furthermore, several corollaries will follow from our results.