NDLI: Applications of the q-Srivastava-Attiya Operator Involving a Certain Family of Bi-Univalent Functions Associated with the Horadam Polynomials

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Applications of the q-Srivastava-Attiya Operator Involving a Certain Family of Bi-Univalent Functions Associated with the Horadam Polynomials

Content Provider	MDPI
Author	Srivastava, Hari Wanas, Abbas Srivastava, Rekha
Copyright Year	2021
Abstract	In this article, by making use of the q-Srivastava-Attiya operator, we introduce and investigate a new family ${SW}_{Σ} (δ, γ, λ, s, t, q, r)$ of normalized holomorphic and bi-univalent functions in the open unit disk $U$ , which are associated with the Bazilevič functions and the $λ$ -pseudo-starlike functions as well as the Horadam polynomials. We estimate the second and the third coefficients in the Taylor-Maclaurin expansions of functions belonging to the holomorphic and bi-univalent function class, which we introduce here. Furthermore, we establish the Fekete-Szegö inequality for functions in the family ${SW}_{Σ} (δ, γ, λ, s, t, q, r)$ . Relevant connections of some of the special cases of the main results with those in several earlier works are also pointed out. Our usage here of the basic or quantum (or q-) extension of the familiar Hurwitz-Lerch zeta function $Φ (z, s, a)$ is justified by the fact that several members of this family of zeta functions possess properties with local or non-local symmetries. Our study of the applications of such quantum (or q-) extensions in this paper is also motivated by the symmetric nature of quantum calculus itself.
Starting Page	1230
e-ISSN	20738994
DOI	10.3390/sym13071230
Journal	Symmetry
Issue Number	7
Volume Number	13
Language	English
Publisher	MDPI
Publisher Date	2021-07-08
Access Restriction	Open
Subject Keyword	Symmetry Logic Holomorphic Functions Univalent Functions Bi-univalent Functions Hurwitz-lerch Zeta Function Srivastava-attiya Operator Bazilevič Functions Λ-pseudo-starlike Functions Horadam Polynomials Taylor-maclaurin Expansions Coefficient Estimates Fekete-szegö Problem Subordination Between Holomorphic Functions Q-srivastava-attiya Operator Hadamard Product (or Convolution)
Content Type	Text
Resource Type	Article

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