Certain subclasses of starlike functions of complex order involving the Hurwitz-Lerch Zeta function

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

Coefficient bounds for some subclasses of p-valently starlike functions

For functions of the form $$f(z) = z^{p} + \sum_{n = 1}^{\infty} a_{p + n} z^{p + n}$$ we obtain sharp bounds for some coefficients functionals in certain subclasses of starlike functions. Certain applications of our main results are also given. In particular, Fekete-Szego-like inequality for classes of functions defined through extended fractional differintegrals are obtained

Coefficient Bounds for Certain Subclasses of Bi-Univalent Function

We introduce two new subclasses of the function class Σ of bi-univalent functions defined in the open unit disc. Furthermore, we find estimates on the coefficients |a2| and |a3| for functions in these new subclasses. Also consequences of the results are pointed out