On New Subclass of Harmonic Univalent Functions Associated with Modified q-Operator

Abstract

In this article, we introduce new subclasses of harmonic univalent functions associated with the q-difference operator. The modified q-Srivastava-Attiya operator is defined and certain applications of this operator are discussed. We investigate the sufficient condition, distortion result, extreme points and invariance of convex combination of the elements of the subclasses.

A Study of Spiral-Like Harmonic Functions Associated with Quantum Calculus

“…where s ∈ ℝ, τ > −1, ς ∈ ½0, 1Þ, jζj < π/2, and q ∈ ð0, 1Þ. Equivalently, we can write (24) as (25) and employing (8) along with (13), and also some computation yields…”

“…with ∑ ∞ n=1 ðν n + Ω n Þ = 1. We follow our required result by substituting the values of ja n j and jb n j from the above relations in (13).…”

“…for n ∈ ℕ = f1, 2, 3, ::g and z ∈ U. For some recent investigations involving q-calculus, we may refer the interested reader to [12][13][14][15][16][17]. Recently, in [18], Shah and Noor introduced the q-analogue of multiplier transformation I s q,τ : A ⟶ A by…”

“…Also, we define HST s,τ q ðζ, ςÞ = HST s,τ q ðζ, ςÞ ∩ S H , where S H denotes the subclass of S H consisting of functions given by (13). It is noted that, for s = τ = 0, we have HST s,τ q ðζ, ςÞ = HST q ðζ, ςÞ and HST s,τ q ðζ, ςÞ = HST q ðζ, ςÞ.…”

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

“…This was the amazing breakthrough by which two different fields, q-calculus and the theory of analytic functions, were linked. After this interesting investigation, certain subclasses of analytic functions were defined and examined in terms of q-function theory by several scholars; we refer to [21][22][23][24][25][26][27][28][29][30]. The study of q-operators plays a vital role in the development of this field of study.…”