The Fekete–Szegö functional associated with k-th root transformation using quasi-subordination

C. Ramachandran1, T. Soupramanien2, Janusz Sokół3
1Department of Mathematics, University College of Engineering Villupuram, Anna University, Villupuram, India
2Department of Mathematics, IFET College of Engineering, Villupuram, India
3Faculty of Mathematics and Natural Sciences, University of Rzeszów, Rzeszów, Poland

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Abdel-Gawad, H.R. 2000. On the Fekete - Szegö problem for alpha-Quasi-convex functions. Tamkang Journal of Mathematics 31 (4): 251–255.

Ahuja, O.P., and M. Jahangiri. 1997. Fekete - Szegö problem for a unified class of analytic functions. Panamerican Mathematical Journal 7 (2): 67–78.

Ali, R.M., S.K. Lee, V. Ravichandran, and S. Subramaniam. 2009. The Fekete-Szego coefficient functional for transforms of analytic functions. Bulletin of the Iranian Mathematical Society 35 (2): 119–142.

Altintaş, O., and S. Owa. 1992. Majorizations and quasi-subordinations for certain analytic functions. Proceedings of the Japan Academy A 68 (7): 181–185.

Cho, N.E., and S. Owa. 2004. On the Fekete - Szegö problem for strongly $$\alpha $$ α -logarithmic Quasiconvex functions. Southeast Asian Bulletin of Mathematics 28 (3): 421–430.

Choi, J.H., Y.C. Kim, and T. Sugawa. 2007. A general approach to the Fekete - Szegö problem. Journal of the Mathematical Society of Japan 59 (3): 707–727.

Darus, M., and D.K. Thomas. 1998. $$\alpha $$ α -logarithmically convex functions. Indian Journal of Pure and Applied Mathematics 29 (10): 1049–1059.

Darus, M., and N. Tuneski. 2003. On the Fekete - Szegö problem for generalized close-to-convex functions. International Mathematical Journal 4 (6): 561–568.

Gurusamy, Palpandy, Janusz Sokól, and Srikandan Sivasubramanian. 2015. The FeketeSzegö functional associated with $$k$$ k -th root transformation using quasi-subordination. Comptes Rendus Mathematique 353 (7): 617–622.

Haji Mohd, M., and M.Darus. 2012. Fekete–Szegö problems for quasi-subordination classes. Abstract and Applied Analysis 2012: 192956-1–192956-14.

Keogh, F.R., and E.P. Merkes. 1969. A coefficient inequality for certain classes of analytic functions. Proceedings of the American Mathematical Society 20: 8–12.

Lee, S.Y. 1975. Quasi-subordinate functions and coefficient conjectures. Journal of the Korean Mathematical Society 12 (1): 43–50.

Lewandowski, Z., S. Miller, and E.Z. Lotkiewicz. 1976. Gamma-starlike functions. Annales Universitatis Mariae Curie-Sk lodowska A 28: 53–58.

Ma W., and Minda D. 1994. A unified treatment of some special classes of univalent functions, in: Proceedings of the Conference on Complex Analysis, (Tianjin, 1992), Conference Proceedings Lecture Notes Analysis, International Press, Cambridge, Mass, USA, 1 (1994), pp 157–169.

Miller, S.S., and P.T. Mocanu. 1981. Differential subordinations and univalent functions. Michigan Mathematical Journal 28: 151–171.

Miller, S.S., and P.T. Mocanu. 2000. Differential subordinations: theory and applications, Series of Monographs and Textbooks in Pure and Applied Mathematics, vol. 225. New York / Basel: Marcel Dekker Inc.

Ramachandran, C., S. Sivasubramanian, H.M. Srivastava, and A. Swaminathan. 2009. Coefficient inequalities for certain subclasses of analytic functions and their applications involving the Owa-Srivastava operator of fractional calculus. Mathematical Inequalities and Applications 12 (2): 351–363.

Ravichandran, V., M. Maslina Darus, M. Hussain Khan, and K.G. Subramanian. 2004. The Fekete-Szego coefficient functional for transforms of analytic functions. Australian Journal of Mathematical Analysis and Applications 1 (2): 7.

Ren, F.Y., S. Owa, and S. Fukui. 1991. Some inequalities on Quasi-subordinate functions. Bulletin of the Australian Mathematical Society 43 (2): 317–324.

Robertson, M.S. 1970. Quasi-subordination and coefficient conjectures. Bulletin of the American Mathematical Soceity 76: 1–9.

Ponnusamy, S. 1990. On a subclass of $$\lambda$$ λ -spiral-like functions. Mathematica (Cluj) 32 (55): no. 1, 67–76.