Filomat 2023 Volume 37, Issue 1, Pages: 85-95
https://doi.org/10.2298/FIL2301085W
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On a family of p-valently analytic functions missing initial Taylor coefficients
Wani Lateef Ahmad (Department of Mathematics, Indian Institute of Technology Roorkee, Uttarakhand, India), lateef17304@gmail.com
For k ≥ 0, 0 ≤ γ ≤ 1, and some convolution operator 1, the object of this
paper is to introduce a generalized family TUnp (1, γ, k, b, α) of
p-valently analytic functions of complex order b ∈ C \ {0} and type α ∈ [0,
p). Apart from studying certain coefficient, radii and subordination
problems, we prove that TUnp (1, γ, k, b, α) is convex and derive its
extreme points. Moreover, the closedness of this family under the modified
Hadamard product is discussed. Several previously established results are
obtained as particular cases of our theorems.
Keywords: p-valently analytic functions, Hadamard product, Subordination, Subordinating factor sequence
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