×

Fekete-Szegő inequality for a subclass of \(p\)-valent analytic functions. (English) Zbl 1273.30012

Summary: The main object of this paper is to study the Fekete-Szegő problem for the class of \(p\)-valent functions. The Fekete-Szegő inequality is obtained for several classes as a special case from our results. Applications of the results are also obtained in a class defined by convolution.

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] R. M. Ali, V. Ravichandran, and N. Seenivasagan, “Coefficient bounds for p-valent functions,” Applied Mathematics and Computation, vol. 187, no. 1, pp. 35-46, 2007. · Zbl 1113.30024
[2] W. C. Ma and D. Minda, “A unified treatment of some special classes of univalent functions,” in Proceedings of the Conference on Complex Analysis, pp. 157-169, International Press, 1994. · Zbl 0823.30007
[3] S. Owa, “Properties of certain integral operators,” Southeast Asian Bulletin of Mathematics, vol. 24, no. 3, pp. 411-419, 2000. · Zbl 0980.30011
[4] V. Ravichandran, A. Gangadharan, and M. Darus, “Fekete-Szeg\Ho inequality for certain class of Bazilevic functions,” Far East Journal of Mathematical Sciences, vol. 15, no. 2, pp. 171-180, 2004. · Zbl 1073.30011
[5] M. P. Chen, “On the regular functions satisfying Re{f(z)/z}>\rho ,” Bulletin of the Institute of Mathematics. Academia Sinica, vol. 3, no. 1, pp. 65-70, 1975. · Zbl 0313.30012
[6] F. R. Keogh and E. P. Merkes, “A coefficient inequality for certain classes of analytic functions,” Proceedings of the American Mathematical Society, vol. 20, pp. 8-12, 1969. · Zbl 0165.09102
[7] D. V. Prokhorov and J. Szynal, “Inverse coefficients for (\alpha ,\beta )-convex functions,” Annales Universitatis Mariae Curie-Skłodowska A, vol. 35, pp. 125-143, 1981. · Zbl 0557.30014
[8] C. Ramachandran, S. Sivasubramanian, and H. Silverman, “Certain coefficient bounds for p-valent functions,” International Journal of Mathematics and Mathematical Sciences, vol. 2007, Article ID 46576, 11 pages, 2007. · Zbl 1139.30307
[9] H. M. Srivastava and A. K. Mishra, “Applications of fractional calculus to parabolic starlike and uniformly convex functions,” Computers & Mathematics with Applications, vol. 39, no. 3-4, pp. 57-69, 2000. · Zbl 0948.30018
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.