On λ-pseudo bi-starlike functions related to some conic domains

Abstract

In this paper we introduce a new class L λ Σ (φ) of λ-pseudo bi-starlike functions and determine the bounds for |a 2 | and |a 3 | where a 2 , a 3 are the initial Taylor coefficients of f ∈ L λ Σ (φ). Furthermore, we estimate the Fekete-Szegö functional for f ∈ L λ Σ (φ).2000 Mathematics Subject Classification: Primary 30C45; Secondary 30C50..

Coefficient bounds for certain subclasses of bi-prestarlike functions associated with the Chebyshev polynomials

“…These polynomials have been studied in several papers from a theoretical point of view. Lately ,there has been triggering interest by introducing a new class of A and discussed coefficient problems and celebrated Fekete-Szegö problem(see [21,26,27,28]) further certain subclasses of Σ were defined by means of these polynomials(see [15,20,22,24] and discussed extensively. Here, in this article, we propose to make use of the Chebyshev polynomials, which is used by us in this paper, play a considerable act in numerical analysis.…”

(U; V )-Lucas polynomial coefficient relations of the bi-univalent function class

“…Corollary 4. Choosing β = 0 and γ = 0 in Theorem 1, that is if θ(ξ) ∈ H B (σ; x), the results which we obtain reduce to Theorem 2.1 in [20].…”

“…These polynomials are important in mathematics due to the fact that they can applicable to number theory, numerical analysis, combinatorics, and other fields. Nowadays, these polyinomials have been studied and different generalizations have been made by many authors: see [1][2][3][5][6][7][8].Also see [13,17,[19][20][21][22][23][24][25][26]28,29,[43][44][45][46].…”

“…(2) Choosing γ = 0 in the class H B (γ, σ; x) we have the class H B (0, σ; x) = H B (σ; x) = L Σ (U; x). The class L Σ (U; x) was studied by Murugusundaramoorthy and Yalçin [20]. This class consists of the function θ ∈ B satisfying…”

Coefficient Bounds and Fekete-Szeg¨o inequality for a Certain Families of Bi-Prestarlike Functions Defined by (M,N)-Lucas Polynomials

“…A function U ∈ A is said to be bi-univalent in O if both U and U −1 are univalent in O, let we name by the notation E the set of bi-univalent functions in O satisfying (1.1). In fact, Srivastava et al [32] refreshed the study of holomorphic and biunivalent functions in recent years, it was followed by other works as those by Frasin and Aouf [15], Altinkaya and Yalçin Journal of Advances in Mathematics Vol 20 (2021) ISSN: 2347-1921 https://rajpub.com/index.php/jam [5], Güney et al [16] and others (see, for example [1,3,8,10,11,18,21,22,23,26,27,28,29,30,31,33,34,35,38,39,41]).…”