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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.38 no.3 Antofagasta ago. 2019

http://dx.doi.org/10.22199/issn.0717-6279-2019-03-0034 

Articles

Radius problem for the class of analytic functions based on Ruscheweyh derivative

1KIIT Deemed to be University, Department of Mathematics, School of Applied Sciences, Bhubaneswar-751024, Odisha, India. e-mail: susanta.k.mohapatra1978@gmail.com

2KIIT Deemed to be University, Department of Mathematics, School of Applied Sciences, Bhubaneswar-751024, Odisha, India. e-mail: trailokyap6@gmail.com

Abstract

Let 𝒜 be the class of analytic functions f (z) with the normalized condition f(0) = f 0(0)−1 = 0 in the open unit disk U. Bymaking use of Ruscheweyh derivative operator, a new subclass 𝒜(β1, β2, β3, β4; λ) of f(z) ∈ 𝒜 satisfying the inequality

for some complex numbers β1, β2, β3, β4 and for some real λ > 0 is introduced. The object of the present paper is to obtain some properties of the function class 𝒜 (β1, β2, β3, β4; λ). Also the radius problems of satisfies the condition is considered.

Keywords: Analytic function; Univalent function; Ruscheweyh derivative; Cauchy-Schwarz inequality; Radius problema; Hölder inequality

Mathematics Subject Classification (2010):  30C45; 30C50

Texto completo disponible sólo en PDF.

Full text available only in PDF format.

Acknowledgment:

The authors would like to thank to the editor and anonymous referees for their comments and suggestions which improve the contents of the manuscript. Further, the present investigation of the second-named autor is supported by CSIR research project scheme no: 25(0278)/17/EMR-II, New Delhi, India.

References

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Received: May 2018; Accepted: March 2019

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