𝐒𝐨𝐦𝐞 𝐏𝐫𝐨𝐩𝐞𝐫𝐭𝐢𝐞𝐬 𝐨𝐟 𝐮𝐧𝐢𝐯𝐚𝐥𝐞𝐧𝐭 𝐟𝐮𝐧𝐜𝐭𝐢𝐨𝐧 𝐰𝐢𝐭𝐡 𝐧𝐞𝐠𝐚𝐭𝐢𝐯𝐞 𝐜𝐨𝐞𝐟𝐟𝐢𝐜𝐢𝐞𝐧𝐭𝐬 𝐝𝐞𝐟𝐢𝐧𝐞𝐝 𝐛𝐲 𝐚 𝐥𝐢𝐧𝐞𝐚𝐫 𝐨𝐩𝐞𝐫𝐚𝐭𝐨𝐫 𝐢𝐧 𝐭𝐡𝐞 𝐨𝐩𝐞𝐧 𝐮𝐧𝐢𝐭 𝐝𝐢𝐬𝐤.

Abstract

In this paper ,we introduce and study the subclass 𝑅𝜆𝛾,𝛿(𝛽,𝜏,𝜎,𝜑) of univalent function with negative coefficients by using new linear operator𝐼𝛾,𝛿(𝑐,𝑏,𝜆) in the open unit disk. We obtain some geometric properties like coefficient inequality ,growth and distortion theorem. Hadmard product ,extreme point, closure theorem and radii of starlikeness, convexity and close-to-convexity of functions belonging to our subclass.