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Certain subclass of alpha-convex bi-univalent functions defined using q -derivative operator

Gagandeep Singh, Gurcharanjit Singh (2025)

Archivum Mathematicum

The present investigation deals with a new subclass of alpha-convex bi-univalent functions in the unit disc E = z : z < 1 defined with q -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.

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

G. Murugusundaramoorthy, K. Uma (2010)

Annales UMCS, Mathematica

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,...

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