Coefficient bounds and second Hankel determinant for a subclass of symmetric bi-starlike functions involving Euler polynomials

New Uses of q-Generalized Janowski Function in q-Bounded Turning Functions

“…The ϱth Hankel determinant of f (z), a concept presented by [34] can be defined when b ≥ 1 and ϱ ≥ 1: [5,[35][36][37]. Srivastava et al [5] recently characterized a fascinating class of bi-univalent functions incorporating Euler polynomials and determined the second Hankel determinant for this specific class. Fekete-Szegö [38] analyzed the Hankel determinant of the function f (z) to have…”

“…In our recent research, we were inspired by Srivastava et al [5] and Polatoglu [33] in 2006 and discovered a novel set of bi-univalent functions by utilizing q-generalized Janowski functions and q-derivative, leading to precise limits for the second Hankel determinant, Fekete-Szegö estimates, and Coefficients Bounds. Additionally, we identified the extremal function for this new class to validate our findings.…”

“…This article provides a summary of q-calculus, first introduced by Jackson and further studied by various mathematicians [5][6][7][8][9][10]. It aims to present essential concepts and definitions in q-calculus and emphasizes the importance of the q-difference operator in fields like geometric function theory.…”

Sharp Bounds on Toeplitz Determinants for Starlike and Convex Functions Associated with Bilinear Transformations

“…Recently, Mandal et al [17] determined the best possible bounds for second Hankel and Hermitian Toeplitz matrices, involving logarithmic coefficients of inverse functions, which are applied to starlike and convex functions concerning symmetric points. In recent studies, considerable attention has been devoted to exploring interesting properties associated with Teoplitz and Hankel determinants within the realm of analytic functions of certain classes of convex and starlike functions (see, for example, [18][19][20][21][22][23][24][25][26][27] and references therein). The Toeplitz determinant, characterized by entries corresponding to the logarithmic coefficients of g ∈ S in the form (14), is expressed as…”