Certain preserving properties of the generalized Alexander operator.
The present investigation deals with a new subclass of alpha-convex bi-univalent functions in the unit disc defined with -derivative operator. Bounds for the first two coefficients and Fekete-Szegö inequality are established for this class. Many known results follow as consequences of the results derived here.
Making use of the Hurwitz-Lerch Zeta function, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients of complex order denoted by TSμ/b (α, β, γ) and obtain coefficient estimates, extreme points, the radii of close to convexity, starlikeness and convexity and neighbourhood results for the class TSμ/b (α, β, γ). In particular, we obtain integral means inequalities for the function f(z) belongs to the class TSμ/b (α, β,...