Abstract
Keeping in view the latest trends toward quantum calculus, due to its various applications in physics and applied mathematics, we introduce a new subclass of meromorphic multivalent functions in Janowski domain with the help of the q-differential operator. Furthermore, we investigate some useful geometric and algebraic properties of these functions. We discuss sufficiency criteria, distortion bounds, coefficient estimates, radius of starlikeness, radius of convexity, inclusion property, and convex combinations via some examples and, for some particular cases of the parameters defined, show the credibility of these results.
Highlights
Introduction and motivationIn the classical calculus, if the limit is replaced by familiarizing the parameter q with limitation 0 < q < 1, the study of such notions is called quantum calculus (q-calculus)
With the help of a certain q-differential operator, we introduce a new subclass of meromorphic multivalent functions involving the Janowski functions
Distortion bounds, coefficient estimates, radius of starlikness, radius of convexity, inclusion property, and convex combinations via some examples, and for some particular cases of the parameters defined, we show the credibility of these results
Summary
Introduction and motivationIn the classical calculus, if the limit is replaced by familiarizing the parameter q with limitation 0 < q < 1, the study of such notions is called quantum calculus (q-calculus). For q ∈ (0, 1), the q-difference operator or q-derivative of a function f is defined by f (ζ ) – f (ζ q) Inspired by the above-mentioned works and [14,15,16,17, 23, 29, 31, 34,35,36,37, 42,43,44], we define the subfamily Mμ,q(p, m, O1, O2) of Mp using the idea of the operator Dμm,q as follows. We can write condition (1.9) as qpζ ∂qDμm,qf (ζ ) [p,q]Dμm,qf (ζ )
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