SUBORDINATION RESULTS FOR A FRACTIONAL INTEGRAL OPERATOR

Abstract

In this paper, we establish several differential subordinations regarding the operator 𝐷^(−𝜆)_𝑧 𝑆𝑅^(𝑚,𝑛) defined using the fractional integral of the differential operator 𝑆𝑅^(𝑚,𝑛), obtained as a convolution product of Salagean operator 𝑆^𝑚 and Ruscheweyh derivative 𝑅^𝑛. By means of the newly obtained operator, a new subclass of analytic functions denoted by 𝒮𝓡_(m,n,𝜆)(𝛿) is introduced and various properties and characteristics of this class are derived, makinguse of the concept of differential subordination.

Keywords

• analytic function
• differential subordination
• fractional integral
• convolution product
• salagean operator
• ruscheweyh derivative