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

Abstract

This article presents a new q-analog integral operator, which generalizes the q-Srivastava–Attiya operator. Using this q-analog operator, we define a family of analytic non-Bazilevic̆ functions, denoted as Tq,τ+1,uμ(ϑ,λ,M,N). Furthermore, we investigate the differential subordination properties of univalent functions using q-calculus, which includes the best dominance, best subordination, and sandwich-type properties. Our results are proven using specialized techniques in differential subordination theory.

The Yamaguchi–Noshiro Type of Bi-Univalent Functions Connected with the Linear q-Convolution Operator

“…For the functions F, H ∈ A defined by To start with, we recall the following differential and integral operators. For 0 < q < 1, El-Deeb et al [2,3] defined the q-convolution operator (see also [4][5][6][7]) for F * H by D q (F * H)(ξ)…”

“…Subsequently, Brannan and Clunie [14] conjectured that |c 2 | ≤ √ 2. Netanyahu [15], on the other hand, showed that max F∈B |c 2 | = 4 3 . The coefficient estimate problem for each of the following Taylor-Maclaurin coefficients:…”

New Subclass of Close-to-Convex Functions Defined by Quantum Difference Operator and Related to Generalized Janowski Function

“…There was a flurry of research on the q-analogues of other differential operators after the introduction of the q-difference operator. Significant work has been carried out in both GFT and q-calculus theory by several mathematicians (for details, see [10][11][12][13][14][15][16][17]). Using the q-difference operator and generalized Janowski functions, we construct a new class of q-close-to-convex functions and explore several unique characteristics of the analytic function f that belongs to this class.…”

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].…”