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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,...

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 $T{S}_b^{\mu }(\alpha ,\beta ,\gamma )$ and obtain coefficient estimates, extreme points, the radii of close to convexity, starlikeness and convexity and neighbourhood results for the class $T{S}_b^{\mu }(\alpha ,\beta ,\gamma )$. In particular, we obtain integral means inequalities for the function $f\left(z\right)$ belongs to the class $T{S}_b^{\mu }(\alpha ,\beta ,\gamma )$ in the unit disc.