The Fekete–Szegö problem for a class of analytic functions defined by Carlson–Shaffer operator

Om P. Ahuja, Halit Orhan

Abstract


In the present investigation we solve Fekete-Szegö problem for the generalized linear differential operator. In particular, our theorems contain corresponding results for various subclasses of strongly starlike and strongly convex functions. In the present investigation we solve Fekete-Szegö problem for the generalized linear differential operator. In particular, our theorems contain corresponding results for various subclasses of strongly starlike and strongly convex functions.

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References


Abdel-Gawad, H. R., Thomas, D. K., Fekete-Szegö problem for strongly close-toconvex function, Proc. Amer. Math. Soc. 114 (2) (1992), 345-349.

Al-Oboudi, F. M., On univalent functions defined by a generalized Sălăgean operator, Int. J. Math. Math. Sci., no. 25–28 (2004), 1429-1436.

Brannan D. A., Kirwan, W. E., On some classes of bounded univalent functions, J. London Math. Soc. 2 (1) (1969), 431-443.

Carlson, B. C., Shaffer, D. B., Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal. 15 (1984), 737-745.

Çağlar, M., Deniz, E., Orhan, H., Coefficient bounds for a subclass of starlike functions of complex order, Appl. Math. Comput. 218 (2011), 693-698.

Darus, M., Akbarally, A., Coefficient estimates for Ruscheweyh derivatives, Int. J. Math. Math. Sci. 36 (2004), 1937-1942.

Deniz, E., Orhan, H., The Fekete-Szegö problem for a generalized subclass of analytic functions, Kyungpook Math. J. 50 (2010), 37-47.

Deniz, E., Çağlar, M., Orhan, H., The Fekete-Szegö problem for a class of analytic functions defined by Dziok-Srivastava operator, Kodai Math. J. 35 (2012), 439-462.

Dziok, J., Classes of functions defined by certain differential-integral operators, J. Comput. Appl. Math. 105 (1999), 245-255.

Fekete, M., Szegö, G., Eine Bermerkung uber ungerade schlichte funktionen, J. London Math. Soc. 8 (1933), 85-89.

Frasin, B., Darus, M., On Fekete–Szegö problem using Hadamard product, Int. J. Math. Math. Sci. 12 (2003), 1289-1295.

Goel, R. M., Mehrok, B. S., A coefficient inequality for certain classes of analytic functions, Tamkang J. Math. 22 (2) (1995), 153-163.

Koeghe, F. R., Merkes, E. P., A coefficient inequality for certain classes of analytic functions, Proc. Amer. Math. Soc. 20 (1969), 8-12.

Lashin, A. Y., Starlike and convex functions of complex order involving a certain linear operator, Indian J. Pure Appl. Math. 34 (7) (2003), 1101-1108.

Orhan, H., Kamali, M., On the Fekete–Szegö problem, Appl. Math. Comput. 144 (2003), 181-186.

Orhan, H., Raducanu, D., Fekete–Szegö problem for strongly starlike functions associated with generalized hypergeometric functions, Math. Comput. Modelling 50 (2009), 430-438.

Orhan, H., Yağmur, N., Deniz, E., Coefficient inequality for a generalized subclass of analytic functions, Bull. Transilv. Univ. Braşov Ser. III 4(53), no. 1 (2011), 51-57.

Orhan, H., Deniz, E., Çağlar, M., Fekete–Szegö problem for certain subclasses of analytic functions, Demonstratio Math. 45, no. 4 (2012), 835-846.

Pommerenke, Ch., Univalent Functions, Vandenhoeck and Ruprecht, Gottingen, 1975.

Răducanu, D., Orhan, H., Subclasses of analytic functions defined by a generalized differential operator, Int. J. Math. Anal. (Ruse) 4 (1) (2010), 1-15.

Ravichandran, V., Kumar, S. S., On a class of analytic functions involving Carlson-Shaffer linear operator, Riv. Math. Univ. Parma 7 (3) (2004), 35-48.

Ruscheweyh, S., New criteria for univalent functions, Proc. Amer. Math. Soc. 49 (1975), 109-115.

Sălăgean, G. S., Subclasses of univalent functions, Complex analysis - fifth Romanian-Finnish seminar, Part 1 (Bucharest, 1981), Lecture Notes in Math. 1013, Springer, Berlin, 1983, 362-372.

Srivastava, H. M., Owa, S. (Eds.), Current Topics in Analytic Fuction Theory, World Scientific Publishing, New Jersey, 1992.

Srivastava, H. M., Mishra, A. K., Das, M. K., The Fekete-Szegö problem for a subclass of close-to-convex functions, Complex Variable Theory Appl. 44 (2) (2001), 145-163.




DOI: http://dx.doi.org/10.2478/umcsmath-2014-0001
Date of publication: 2015-05-23 16:29:35
Date of submission: 2015-05-04 20:54:50


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