List of issues > Series «Mathematics». 2018. Vol. 23
On Certain Subclasses of Analytic Functions with Varying Arguments of Coefficients
In this paper we introduce and study the class ? ℛ δ, η(n, λ, α) of analytic functions with varying arguments of coefficients. We obtain coefficients inequalities, distortion theorems involving fractional calculus, radii of close to convexity, starlikeness and convexity and square root transformation for functions in the class ? ℛ δ, η(n, λ, α). Finally, integral convolution for functions in this class are considered.
About the Authors
Hanaa Mosa Ahmed Zayed, Ph. D. Student, Department of Mathematics, Faculty of Science, Menofia University, Shebin Elkom 32511, Egypt, e-mail: hanaazayed42@yahoo.com
Mohamed Kamal Aouf, Prof., Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt, e-mail: mkaouf127@yahoo.com
Maslina Darus, Prof. of School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia Bangi 43600 Selangor D. Ehsan, Malaysia, e-mail: maslina@ukm.edu.my
1. Aouf M.K. On fractional derivatives and fractional integrals of certain subclasses of starlike and convex functions. Math. Japon., 1990, vol. 35, no 5, pp. 831-837.
2. Duren P.L. Univalent Functions. Springer-Verlag, New York, 1983.
3. Owa S. On the distortion theorems. I. Kyungpook Math. J., 1978, vol. 18, no 1, pp. 53-59.
4. Silverman H. Univalent functions with varying arguments, Houston J. Math., 1981, vol. 7, no 2, pp. 283-287.
5. Srivastava H.M., Aouf M.K. A certain fractional derivative operator and its applica-tions to a new class of analytic and multivalent functions with negative coefficients. I and II, J. Math. Anal. Appl., 1992, vol. 171, pp. 1-13 ibid. 1995, 192, pp. 973-688.
6. Srivastava H.M., Aouf M.K. Some applications of fractional calculus operatorsto certain subclasses of prestarlike functions with negative coefficients. ComputersMath. Appl., 1995, vol. 30, no 1, pp. 53-61. https://doi.org/10.1016/0898-1221(95)00067-9
7. Srivastava H.M., Owa S. An application of the fractional derivative, Math. Japon.,1984, vol. 29, pp. 383-389.
8. Srivastava H.M., Owa S. (eds.). Univalent Functions, Fractional Calculus and Their Applications. Halsted press (Ellis Horwood Limited Chichester). John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1989.
9. Srivastava H. M., Owa S. (eds.). Current Topics in Analytic Function Theory. World Scientific Publishing Company, Singapore, New Jersey, London, and Hong Kong, 1992. https://doi.org/10.1142/1628
10. Uralegaddi B.A., Ganigi M.D., Sarangi S.M. Close to convex functions with positive coefficients. Stud. Univ. Babes-Bolyai Math., 1995, pp. 25-31.