Fekete-Szegö problem for generalized bi-subordinate functions of complex order

Abstract

In this paper, we obtain the Fekete-Szegö inequality for the generalized bi-subordinate functions of complex order. The various results, which are presented in this paper, would generalize those in related works of several earlier authors.

Bi-univalent functions of order ζ connected with ( m , n ) -Lucas polynomials

“…Remark 2.19. Setting q → 1−, r = k = s = η = 1, and replacing G m,n (z) − 1 by Φ(z), such that Φ(0) = 1 and Φ (0) 0, in Theorems 2.6 and 2.11, then we deduce Theorems 2.3 and 2.4, that have been investigated by Kazımo glu and Deniz [25].…”

“…The Bieberbach conjecture-related Fekete-Szeg ö problem centers on an inequality for the coefficients of univalent functions f in (1.1), that have been discovered by Fekete and Szeg ö [18]. The inequality consists of determining an estimate of the maximum value of the coefficient functional a 3 − ξa 2 2 (see [10,12,15,21,25,29,31,32]).…”

Fekete-Szegö Inequality for Certain Subclasses of Analytic Functions Defined by The Combination of Differential and Integral Operators

“…  and Chonweerayoot et al, 1992;Darus and Thomas, 1996;Darus and Thomas, 1998;Keogh and Merkes, 1969;Koepf, 1987;London, 1993;Ma and Minda, 1994) and (see also recent research on this subject by (Çağlar and Orhan, 2021;Deniz et al, 2012;Kanas and Darwish, 2010;Kazımoğlu and Deniz, 2020 ; Kazımoğlu and Mustafa, 2020; Orhan et al, 2010; Orhan and Răducanu, 2009)).…”

Investigating New Subclasses of Bi-Univalent Functions Associated with q-Pascal Distribution Series Using the Subordination Principle

“…They discovered estimates for the initial coefficients of functions in them. However, as mentioned in a few places ( [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45]), the problem of sharp coefficient bounds for |a n |,…”