On Generalizations of the Close-to-Convex Functions Associated with q-Srivastava–Attiya Operator

Abstract

The study of the q-analogue of the classical results of geometric function theory is currently of great interest to scholars. In this article, we define generalized classes of close-to-convex functions and quasi-convex functions with the help of the q-difference operator. Moreover, by using the q-analogues of a certain family of linear operators, the classes Kq,bsh, K˜q,sbh, Qq,bsh, and Q˜q,sbh are introduced. Several interesting inclusion relationships between these newly defined classes are discussed, and the invariance of these classes under the q-Bernadi integral operator was examined. Furthermore, some special cases and useful consequences of these investigations were taken into consideration.

Sandwich-Type Theorems for a Family of Non-Bazilevič Functions Involving a q-Analog Integral Operator

“…Let κ 1 (z) and κ 2 (z) be convex functions in U, with κ 1 (0) = κ 2 (0) = 1, and let ϑ ∈ C with R(ϑ) > 0. Let κ 2 (z) satisfy the conditions in (27), (28)…”

“…Recently, intriguing findings have been published regarding the use of an integral operator, as evidenced in [28]. Building on these findings, and inspired by previous results obtained by applying q-calculus to various derivative and integral operators (as seen in [29][30][31]), we decided to extend our study to the q-Srivastava-Attiya operator in this paper.…”

Applications of q-Calculus Multiplier Operators and Subordination for the Study of Particular Analytic Function Subclasses

“…Furthermore, q-difference operators were investigated in [16][17][18]; fractional calculus aspects were added to the studies regarding q-calculus in [19][20][21]; and a q-integral operator was used for studies in [22]. The q-Srivastava-Attiya operator is used for investigation on the class of close-to-convex functions in [23], and a q-analogue integral operator is applied for a family of non-Bazilevič functions in [24]. A q-analogue of a multiplier transformation is used for obtaining new differential subordination and superordination results in [25].…”