Some applications of generalized Ruscheweyh derivatives involving a general fractional derivative operator to a class of analytic functions with negative coefficients I

For certain univalent function f, we study a class of functions f as defined by making use of the generalized Ruscheweyh derivatives involving a general fractional derivative operator, satisfying Re { (zJ1λ, μ f(z))')/((1 -γ) J1λ, μ f(z) + γ z2(J1λ, μ f(z))" )} > β. A necessary and sufficient condition for a function to be in the class Aγλ, μ, ν(n, β) is obtained. In addition, our paper includes distortion theorem, radii of starlikeness, convexity and close-to-convexity, extreme points. Also, we get some results in this paper.