New Applications of the Bernardi Integral Operator.

Let A (p , n) be the class of f (z) which are analytic p-valent functions in the closed unit disk U ¯ = z ∈ C : z ≤ 1 . The expression B − m − λ f (z) is defined by using fractional integrals of order λ for f (z) ∈ A (p , n). When m = 1 and λ = 0 , B − 1 f (z) becomes Bernardi integral operator. Using the fractional integral B − m − λ f (z) , the subclass T p , n α s , β , ρ ; m , λ of A (p , n) is introduced. In the present paper, we discuss some interesting properties for f (z) concerning with the class T p , n α s , β , ρ ; m , λ. Also, some interesting examples for our results will be considered. [ABSTRACT FROM AUTHOR]