Some Properties of Analytic Functions with the Fixed Second Coefficients

ABSTRACT

In this paper, we investigate some argument properties for analytic functions with fixed second coefficient and positive real part. And we apply the argument properties to the functions that are analytic and normalized. In particular, the order of strongly starlikeness of strongly convex functions with fixed second coefficients is given.

KEYWORDS

Analytic Functions, Argument Estimate, Fixed Second Coefficients, Strongly Starlike Functions, Strongly Convex Functions

Analytic Functions, Argument Estimate, Fixed Second Coefficients, Strongly Starlike Functions, Strongly Convex Functions

Cite this paper

Kwon, O. (2014) Some Properties of Analytic Functions with the Fixed Second Coefficients.*Advances in Pure Mathematics*, **4**, 194-202. doi: 10.4236/apm.2014.45025.

Kwon, O. (2014) Some Properties of Analytic Functions with the Fixed Second Coefficients.

References

[1] Nunokawa, M. (1992) On Properties of Non-Caratheodory Functions. Proceedings of the Japan Academy, Series A, Mathematical Sciences, 68, 152-153.

[2] Nunokawa, M. (1993) On the Order of Strongly Starlikeness of Strongly Convex Functions. Proceedings of the Japan Academy, Series A, Mathematical Sciences, 69, 234-237.

[3] Ali, R.M., Nagpal, S. and Ravichandran, V. (2011) Second-Order Differential Subordination for Analytic Functions with Fixed Initial Coefficient. Bulletin of the Malaysian Mathematical Sciences Society, 34, 611-629.

[4] Ali, R.M., Cho, N.E., Jain, N. and Ravichandran, V. (2012) Radii of Starlikeness and Convexity of Functions Defined by Subordination with Fixed Second Coefficients, Filomat, 26, 553-561.

http://dx.doi.org/10.2298/FIL1203553A

[5] Miller, S.S. and Mocanu, P.T. (2000) Differential Subordinations. Dekker, New York.

[6] Lee, S.K., Ravichandran, V. and Supramaniam, S. (2012) Applications of Differential Subordination for Functions with Fixed Coefficient to Geometric Function Theory. arXiv:1209.0896.

[7] Nagpal, S. and Ravichandran, V. (2012) Applications of Theory of Differential Subordinatioin for Functions with Fixed Initial Coefficient to Univalent Functions. Annales Polonici Mathematici, 105, 225-238.

http://dx.doi.org/10.4064/ap105-3-2

[8] Nunokawa, M., Owa, S., Hayami, T., Kuroki, K. and Uyanik, N. (2011) Some Conditions for Strongly Starlikeness of Certain Analytic Functions. International Mathematical Forum, 6, 1199-1208.

[9] Nunokawa, M., Owa, S. and Saitoh, H. (2003) Argument Estimates for Certain Analytic Functions. Proceedings of the Japan Academy, Series A, Mathematical Sciences, 79, 163-166.

[1] Nunokawa, M. (1992) On Properties of Non-Caratheodory Functions. Proceedings of the Japan Academy, Series A, Mathematical Sciences, 68, 152-153.

[2] Nunokawa, M. (1993) On the Order of Strongly Starlikeness of Strongly Convex Functions. Proceedings of the Japan Academy, Series A, Mathematical Sciences, 69, 234-237.

[3] Ali, R.M., Nagpal, S. and Ravichandran, V. (2011) Second-Order Differential Subordination for Analytic Functions with Fixed Initial Coefficient. Bulletin of the Malaysian Mathematical Sciences Society, 34, 611-629.

[4] Ali, R.M., Cho, N.E., Jain, N. and Ravichandran, V. (2012) Radii of Starlikeness and Convexity of Functions Defined by Subordination with Fixed Second Coefficients, Filomat, 26, 553-561.

http://dx.doi.org/10.2298/FIL1203553A

[5] Miller, S.S. and Mocanu, P.T. (2000) Differential Subordinations. Dekker, New York.

[6] Lee, S.K., Ravichandran, V. and Supramaniam, S. (2012) Applications of Differential Subordination for Functions with Fixed Coefficient to Geometric Function Theory. arXiv:1209.0896.

[7] Nagpal, S. and Ravichandran, V. (2012) Applications of Theory of Differential Subordinatioin for Functions with Fixed Initial Coefficient to Univalent Functions. Annales Polonici Mathematici, 105, 225-238.

http://dx.doi.org/10.4064/ap105-3-2

[8] Nunokawa, M., Owa, S., Hayami, T., Kuroki, K. and Uyanik, N. (2011) Some Conditions for Strongly Starlikeness of Certain Analytic Functions. International Mathematical Forum, 6, 1199-1208.

[9] Nunokawa, M., Owa, S. and Saitoh, H. (2003) Argument Estimates for Certain Analytic Functions. Proceedings of the Japan Academy, Series A, Mathematical Sciences, 79, 163-166.