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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

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


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:

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


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

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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.


[1] O. Kwon, Y. Sim, N. Cho, and H. Srivastava, “Some radius problems related to a certain subclass of analytic functions”,Acta Mathematica Sinica, English Series, vol. 30, no. 7, pp. 1133-1144, Jul. 2014, doi: 10.1007/s10114-014-3100-0. [ Links ]

[2] S. Maharana, J. Prajapat, and H. Srivastava, “The radius of convexity of partial sums of convex functions in one direction”, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, vol. 87, no. 2, pp. 215-219, Feb. 2017, doi: 10.1007/s40010-017-0348-7. [ Links ]

[3] S. Ruscheweyh, “New criteria for univalent functions”,Proceedings of the American Mathematical Society, vol. 49, no. 1, pp. 109-109, Jan. 1975, doi: 10.1090/S0002-9939-1975-0367176-1. [ Links ]

[4] H. Silverman, “Univalent functions with negative coefficients”, Proceedings of the American Mathematical Society , vol. 51, no. 1, pp. 109-109, Jan. 1975, doi: 10.1090/S0002-9939-1975-0369678-0. [ Links ]

[5] H. Srivastava, N. Xu, and D. Yang, “Inclusion relations and convolution properties of a certain class of analytic functions associated with the Ruscheweyh derivatives”, Journal of Mathematical Analysis and Applications, vol. 331, no. 1, pp. 686-700, Jul. 2007, doi: 10.1016/j.jmaa.2006.09.019. [ Links ]

[6] N. Uyanìk, S. Owa, and E. Kadioǧlu, “Some properties of functions associated with close-to-convex and starlike of order”,Applied Mathematics and Computation, vol. 216, no. 2, pp. 381-387, Mar. 2010, doi: 10.1016/j.amc.2010.01.022. [ Links ]

[7] N. Uyanìk and S. Owa, “New extensions for classes of analytic functions associated with close-to-convex and starlike of order α”,Mathematical and Computer Modelling, vol. 54, no. 1-2, pp. 359-366, Jul. 2011, doi: 10.1016/j.mcm.2011.02.020 [ Links ]

Received: May 2018; Accepted: March 2019

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