Abstract
In this present paper, we introduce and explore certain new classes of uniformly convex and starlike functions related to the Liu–Owa integral operator. We explore various properties and characteristics, such as coefficient estimates, rate of growth, distortion result, radii of close-to-convexity, starlikeness, convexity, and Hadamard product. It is important to mention that our results are a generalization of the number of existing results in the literature.
Highlights
Let C denote the complex plane and assume that Ap denotes the class of p-valent function of the form ∞λ(ω) ωp + at+pωt+p (p ∈ N {1, 2, . . .}), (1)t 1 which are analytic in the open unit disc ⋓ {ω: ω ∈ C and |ω| < 1
Taking from the above cited work and using Liu–Owa integral operator, we introduce the following class of p-valent analytic function
We have presented and studied thoroughly some new subclasses of p− valent functions related with uniformly convex and starlike functions, in connection with the Liu–Owa integral operator Qab,pλ(ω) given by (8)
Summary
Syed Ghoos Ali Shah ,1 Saqib Hussain ,1 Saima Noor, Maslina Darus ,3 and Ibrar Ahmad. Received 15 August 2021; Revised September 2021; Accepted September 2021; Published 6 December 2021. In this present paper, we introduce and explore certain new classes of uniformly convex and starlike functions related to the Liu–Owa integral operator. We explore various properties and characteristics, such as coefficient estimates, rate of growth, distortion result, radii of close-to-convexity, starlikeness, convexity, and Hadamard product. It is important to mention that our results are a generalization of the number of existing results in the literature
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