Abstract
This paper deals with a new subclass of univalent function associated with the right half of the lemniscate of Bernoulli. We find the upper bound of the Hankel determinant H3(1) for this subclass by applying the Carlson–Shaffer operator to it. The present work also deals with certain properties of this newly defined subclass, such as the upper bound of the Hankel determinant of order 3, coefficient estimates, etc.
Highlights
Associated with Lemniscate of Suppose that H( E) represents the class of those functions that are analytic in any open unit disk, i.e.,E = {z : z ∈ C such that |z| < 1}.Bernoulli
Our main focus in this work is for the class SL∗ (α, β) on the Hankel determinant H3 (1)
We introduced a new subclass of univalent function associated with a Carlson–Shaffer operator, named as SL∗ (α, β)
Summary
Associated with Lemniscate of Suppose that H( E) represents the class of those functions that are analytic in any open unit disk, i.e.,. We denote the class A of those analytic functions, which satisfies. We represent by S ∗ , the class of starlike function in E, which satisfies creativecommons.org/licenses/by/. SL∗ represents the class of those functions that satisfying z f 0 (z). Suppose that SL∗ (α, β) is the subclass of analytic functions given by. For a subclass of analytic functions, the Hankel determinant of H3 (1) was studied by Babalola [9]. Our main focus in this work is for the class SL∗ (α, β) on the Hankel determinant H3 (1)
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