Starlike and Convex Functions Associated with a Nephroid Domain

Wani, Lateef Ahmad; Swaminathan, A.

doi:10.1007/s40840-020-00935-6

Cited by 71 publications

(43 citation statements)

References 23 publications

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“…, where ψ(z) � 1 + z − z 3 /3, was introduced and studied by Wani and Swaminathan in [22]. Geometrically, f ∈ S * N e provided zf ′ (z)/f(z) lies in the region bounded by the nephroid: a 2-cusped kidneyshaped curve Ω N e ≔ w � u + iv:…”

Section: Proofmentioning

confidence: 99%

Starlikeness of Analytic Functions with Subordinate Ratios

Ali

Ravichandran

Sharma

2021

Journal of Mathematics

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Let h be a nonvanishing analytic function in the open unit disc with h 0 = 1 . Consider the class consisting of normalized analytic functions f whose ratios f z / g z , g z / z p z , and p z are each subordinate to h for some analytic functions g and p . The radius of starlikeness of order α is obtained for this class when h is chosen to be either h z = 1 + z or h z = e z . Further, starlikeness radii are also obtained for each of these two classes, which include the radius of Janowski starlikeness, and the radius of parabolic starlikeness.

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Section: Proofmentioning

confidence: 99%

Starlikeness of Analytic Functions with Subordinate Ratios

Ali

Ravichandran

Sharma

2021

Journal of Mathematics

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“…Hence, R e ξz − 1 ξz ≥ 1=ρ e ð−1Þ ¼ 1 2 : Our design is generated by the Caratheodory functions, which are operated in [19]. In this situation, we establish the necessary conditions of the joining bounds of Ψ(z) consuming a Caratheodory function.…”

Section: And a Convex Functionmentioning

confidence: 99%

A new analytic solution of complex Langevin differential equations

Ibrahim

2021

AJMS

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PurposeIn this study, the authors introduce a solvability of special type of Langevin differential equations (LDEs) in virtue of geometric function theory. The analytic solutions of the LDEs are considered by utilizing the Caratheodory functions joining the subordination concept. A class of Caratheodory functions involving special functions gives the upper bound solution.Design/methodology/approachThe methodology is based on the geometric function theory.FindingsThe authors present a new analytic function for a class of complex LDEs.Originality/valueThe authors introduced a new class of complex differential equation, presented a new technique to indicate the analytic solution and used some special functions.

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“…In 2020, Wani and Swaminathan [22] studied the class of starlike functions associated with a nephroid domain, S * N e = S * (ϕ N e ) with ϕ N e (z) = 1 + z − z 3 /3. Goel and Kumar [8] explored various properties of the class S * SG = S * (2/(1 + e −z )) known as the class of starlike functions associated with modified sigmoid function.…”

Section: Introductionmentioning

confidence: 99%

Starlikeness of a product of starlike functions with non-vanishing polynomials

Malik¹,

Ravichandran²

2022

Preprint

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For a function f starlike of order α, 0 α < 1, a non-constant polynomial Q of degree n which is non-vanishing in the unit disc D and β > 0, we consider the functionand find the largest value of r ∈ (0, 1] such that r −1 F (rz) lies in various known subclasses of starlike functions such as the class of starlike functions of order λ, the classes of starlike functions associated with the exponential function, cardioid, a rational function, nephroid domain and modified sigmoid function. Our radii results are sharp. We also discuss the correlation with known radii results as special cases.

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Starlike and Convex Functions Associated with a Nephroid Domain

Cited by 71 publications

References 23 publications

Starlikeness of Analytic Functions with Subordinate Ratios

Starlikeness of Analytic Functions with Subordinate Ratios

A new analytic solution of complex Langevin differential equations

Starlikeness of a product of starlike functions with non-vanishing polynomials

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