Properties of Functions Involving Struve Function

Abstract

Let f ( z ) = z + ∑ n = 2 ∞ a n z n and g p , b , c ( z ) = z + ∑ n = 2 ∞ ( − c 4 ) n − 1 ( 3 2 ) n − 1 ( k ) n − 1 z n with p , b , c ∈ ℂ , k = p + b + 2 2 ≠ 0 , − 1 , − 2 , … be two analytic functions in the unit disk U = { z : | z | < 1 } . This paper gives conditions so that the function T p , b , c ( z ) = ( f ∗ g ) ( z ) , a function associated with the Struve function, is univalent, starlike, or convex in the unit disk.

Keywords

• analytic
• univalent
• Struve function