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

Authors

DOI:

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

Keywords:

Analytic function, Univalent function, Ruscheweyh derivative, Cauchy-Schwarz inequality, Radius problema, Hölder inequality

Abstract

Let ? 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 ?(β1, β2, β3, β4; λ) of f(z) ∈ ? satisfying the inequality

Author Biographies

Trailokya Panigrahi, KIIT Deemed to be University.

Department of Mathematics, School of Applied Sciences.

S. K. Mohapatra, KIIT Deemed to be University.

Department of Mathematics, School of Applied Sciences.

References

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.

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.

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.

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.

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.

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.

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.

Published

2019-08-14

How to Cite

[1]
T. Panigrahi and S. K. Mohapatra, “Radius problem for the class of analytic functions based on Ruscheweyh derivative”, Proyecciones (Antofagasta, On line), vol. 38, no. 3, pp. 537-551, Aug. 2019.

Issue

Section

Artículos