Certain subclasses of analytic functions with complex order associated with generalized Bessel functions

Abstract

In this paper, we obtain the necessary and sufficient conditions for generalized Bessel functions of the first kind zup(z) to be in the classes S(b, λ, β) and R(b, λ, β) of analytic functions with complex order and also give the necessary and sufficient conditions for z(2−up(z)) to be in the classes TS(b, λ, β) and TR(b, λ, β). Furthermore, we give the necessary and sufficient conditions for J(k, c) to be in the class TR(b, λ, β) provided that the function f is in the class Rτ (A, B). Finally, we give conditions for the integral operator G(k, c, z) = ∫0z(2 − up(t))dt to be in the class TR(b, λ, β). Several corollaries and consequences of the main results are also obtained.