Subclasses of p-valent k-uniformly convex and starlike funcitons defined by the q-derivative operator




Ali, Ekram E.
Srivastava, Hari M.
Albalahi, Abeer M.

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The potential for widespread applications of the geometric and mapping properties of functions of a complex variable has motivated this article. On the other hand, the basic or quantum (or q-) derivatives and the basic or quantum (or q-) integrals are extensively applied in many different areas of the mathematical, physical and engineering sciences. Here, in this article, we first apply the q-calculus in order to introduce the q-derivative operator Sⁿₙ ₚᵐq. Secondly, by means of this q-derivative operator, we define an interesting subclass Tℵⁿₗ,ᵐₚ(η,α,κ) of the class of normalized analytic and multivalent (or p-valent) functions in the open unit disk U. This p-valent analytic function class is associated with the class k-UCV of k-uniformly convex functions and the class k-UST of k-uniformly starlike functions in U. For functions belonging to the normalized analytic and multivalent (or p-valent) function class Tℵⁿₗ,ᵐₚ(η,α,κ), we then investigate such properties as those involving (for example) the coefficient bounds, distortion results, convex linear combinations, and the radii of starlikeness, convexity and close-to-convexity. We also consider a number of corollaries and consequences of the main findings, which we derived herein.



a nalytic functions, multivalent (or p-valent) functions, uniformly convex functions, uniformly starlike functions, basic or quantum (or q-) analysis, q-derivative operator, hadamard product (or convolution), generalized q-hypergeometric function


Ali, E. E., Srivastava, H. M., & Albalahi, A. M. (2023). Subclasses of p-valent κ-uniformly convex and starlike functions defined by the q-derivative operator. Mathematics, 11(11), 2578.