Fekete-Szego estimates and second Hankel determinant for a generalized subfamily of analytic functions defined by q-differential operator

Abstract

In this paper, we considered a family of analytic and univalent functions having positive real parts in the unit disk and defined by a q-difference operator. The coefficients, the Fekete-Szego estimates and the second Hankel determinants were established for the family of functions. Our family of functions generalized some earlier known ones and by varying some parameters, our results also generalized some known ones.

Initial coefficient bounds and second Hankel determinant for a certain class of bi-univalent functions using Chebyshev polynomials

“…Also, Brannan and Taha [5] introduced certain subclasses of bi-univalent functions called bi-starlike function of order α and bi-convex function of order α. For example see [1,4,10,15,18] for more background details.…”

“…Fekete and Szegö [8] introduced the generalised the functional |a 3 − λa 2 2 |, where λ is a real number. Some works on this functional can be found in [2,3,10,17,18].…”

Coefficient bounds for regular and bi-univalent functions linked with Gegenbauer polynomials

“…Through corollaries of our main results, we have highlighted many interesting new consequences. The special families examined in this research paper linked with Gegenbauer polynomials could inspire further research related to other aspects such as families using q-derivative operator [8], [18] and [31], q-integral operator [16], meromorphic bi-univalent function families associated with Al-Oboudi differential operator [22] and families using integro-differential operators [21]. Hankel determinant [23] for the defined special families could also be examined.…”

Coefficient estimates for certain class of bi-univalent functions associated with κ-Fibonacci numbers

“…Ismail et al [13] first introduced a class of generalized complex function on subclasses of the analytic function via basic (or q-) calculus. Recently many newsworthy results related to bi-univalent functions and basic (or q-) calculus are meticulously studied by Srivastava et al [30], also refer ( [7], [17], [31]) and the references therein.…”