Janowski starlikeness for a class of analytic functions

The Bessel–Struve kernel function defined in the unit disc is used in this study. The Bessel–Struve kernel functions are generalized in this article, and differential equations are derived. We found conditions under which the generalized Bessel–Struve function is Lemniscate convex by using a subordination technique. The relation between the Janowski class and exponential class is also derived.

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“…These are all classes that have been widely studied; see, for example, in the works of [20][21][22].…”

Section: Basic Concept Of Geometric Properties and Require Lemmasmentioning

confidence: 99%

On Geometric Properties of Bessel–Struve Kernel Functions in Unit Disc

Alarifi

Mondal²

2022

Mathematics

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“…In relation to P[A, B] several subclasses of A were defined, for example S * [A, B], which is called a class of Janowski starlike functions [10] and that consists of f ∈ A satisfying |zf ′ (z)/f (z) − 1| < β|zf ′ (z)/f (z) + 1|}. These classes have been studied, for example, in [1,2]. A function f ∈ A is said to be close-to-convex of order β if Re (zf ′ (z)/g(z)) > β for some g ∈ S * := S * (0) [9,15].…”

Section: Introductionmentioning

confidence: 99%

Relations between the generalized Bessel functions and the Janowski class

Kanas¹,

Mondal²,

Mohammed³

2018

Mathematical Inequalities &Amp; Applications

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We are interested in finding the sufficient conditions on A, B, λ, b and c which ensure that the generalized Bessel functions u λ := u λ,b,c satisfies the subordination u λ (z) ≺ (1 + Az)/(1 + Bz). Also, conditions for which u λ (z) to be Janowski convex, and zu ′ λ (z) to be Janowski starlike in the unit disk D = {z ∈ C : |z| < 1} are obtained.2010 Mathematics Subject Classification. 34B30, 33C10, 30C80, 30C45.

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“…These classes have been studied, for example, in [1,2]. A function f ∈ A is said to be close-to-convex of order β [7,12] if Re (zf ′ (z)/g(z)) > β for some g ∈ S * := S * (0).…”

Section: Introductionmentioning

confidence: 99%

Inclusion of the Generalized Bessel Functions in the Janowski Class

Mondal

Dhuain

2016

International Journal of Analysis

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Sufficient conditions on A, B, p, b and c are determined that will ensure the generalized Bessel functions u p,b,c satisfies the subordination u p,b,c (z) ≺ (1 + Az)/(1 + Bz). In particular this gives conditions for (−4κ/c)(u p,b,c (z) − 1), c = 0 to be close-to-convex. Also, conditions for which u p,b,c (z) to be Janowski convex, and zu p,b,c (z) to be Janowski starlike in the unit disk D = {z ∈ C : |z| < 1} are obtained.

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Janowski starlikeness for a class of analytic functions

Cited by 14 publications

References 8 publications

On Geometric Properties of Bessel–Struve Kernel Functions in Unit Disc

On Geometric Properties of Bessel–Struve Kernel Functions in Unit Disc

Relations between the generalized Bessel functions and the Janowski class

Inclusion of the Generalized Bessel Functions in the Janowski Class

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