Some Properties of the Class of Univalent Functions with Negative Coefficients

Affiliation(s)

School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi, Malaysia.

School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi, Malaysia.

ABSTRACT

The main object of this paper is to study some properties of certain subclass of analytic functions with negative coefficients defined by a linear operator in the open unit disc. These properties include the coefficient estimates, closure properties, distortion theorems and integral operators.

The main object of this paper is to study some properties of certain subclass of analytic functions with negative coefficients defined by a linear operator in the open unit disc. These properties include the coefficient estimates, closure properties, distortion theorems and integral operators.

Cite this paper

A. Amer and M. Darus, "Some Properties of the Class of Univalent Functions with Negative Coefficients,"*Applied Mathematics*, Vol. 3 No. 12, 2012, pp. 1851-1856. doi: 10.4236/am.2012.312251.

A. Amer and M. Darus, "Some Properties of the Class of Univalent Functions with Negative Coefficients,"

References

[1] B. C. Carlson and D. B. Shaffer, “Starlike and Prestarlike Hypergeometric Functions,” SIAM Journal on Mathe matical Analysis, Vol. 15, No. 4, 1984, pp. 737-745. doi:10.1137/0515057

[2] A. Catas, “On a Certain Differential Sandwich Theorem Associated with a New Generalized Derivative Operator,” General Mathematics, Vol. 17, No. 4, 2009, pp. 83-95.

[3] A. A. Amer and M. Darus, “A Distortion Theorem for a Certain Class of Bazilevic Function,” International Journal of Mathematical Analysis, Vol. 6, No. 12, 2012, pp. 591-597.

[4] A. A. Amer and M. Darus, “On a Property of a Subclass of Bazilevic Functions,” Missouri Journal of Mathematical Sciences, In Press.

[5] St. Ruscheweyh, “New Criteria for Univalent Functions,” Proceedings of the American Mathematical Society, Vol. 49, No. 1, 1975, pp. 109-115.

[6] G. S. Salagean, “Subclasses of Univalent Functions,” Lecture Notes in Mathematics, Vol. 1013, 1983, pp. 362-372. doi:10.1007/BFb0066543

[7] F. M. Al-Oboudi, “On Univalent Functions Defined by a Generalized Salagean Operator,” International Journal of Mathematics and Mathematical Sciences, Vol. 2004, No. 27, 2004, pp. 1429-1436. doi:10.1155/S0161171204108090

[8] A. W. Goodman, “Univalent Functions and Nonanalytic Curves,” Proceedings of the American Mathematical Society, Vol. 8, No. 3, 1957, pp. 598-601. doi:10.1090/S0002-9939-1957-0086879-9

[9] St. Ruscheweyh, “Neighborhoods of Univalent Functions,” Proceedings of the American Mathematical Society, Vol. 81, No. 4, 1981, pp. 521-527. doi:10.1090/S0002-9939-1981-0601721-6

[10] O. Alintas, H. Irmak and H. M. Srivastava, “Fractional Calculus and Certain Starlike Functions with Negative Coefficietns,” Computers & Mathematics with Applications, Vol. 30, No. 2, 1995, pp. 9-15. doi:10.1016/0898-1221(95)00073-8

[11] O. Alintas, “On a Subclass of Certain Starlike Functions with Negative Coefficients,” Journal of the Mathematical Society of Japan, Vol. 36, 1991, pp. 489-495.

[12] H. Silverman, “Univalent Functions with Negative Coefficients,” Proceedings of the American Mathematical Society, Vol. 51, No. 1, 1975, pp. 109-116. doi:10.1090/S0002-9939-1975-0369678-0

[13] S. K. Chatterjea, “On Starlike Functions,” Journal of Pure Mathematics, Vol. 1, 1981, pp. 23-26.

[14] H. M. Srivastava, S. Owa and S. K. Chatterjea, “A Note on Certain Classes of Starlike Functions,” Rendiconti del Seminario Matematico della Università di Padova, Vol. 77, 1987, pp.115-124.

[15] M. D. Hur and G. H. Oh, “On Certain Class of Analytic Functions with Negative Coefficients,” Pusan Kyongnam Mathematical Journal, Vol. 5, No. 1, 1989, pp. 69-80.

[16] M. Kamali, “Neighborhoods of a New Class of p-Valently Functions with Negative Coefficients,” Mathematical Inequalities & Applications, Vol. 9, No. 4, 2006, pp. 661-670. doi:10.7153/mia-09-59

[17] A. Catas, “Neighborhoods of a Certain Class of Analytic Functions with Negative Coefficients,” Banach Journal of Mathematical Analysis, Vol. 3, No. 1, 2009, pp. 111-121.

[1] B. C. Carlson and D. B. Shaffer, “Starlike and Prestarlike Hypergeometric Functions,” SIAM Journal on Mathe matical Analysis, Vol. 15, No. 4, 1984, pp. 737-745. doi:10.1137/0515057

[2] A. Catas, “On a Certain Differential Sandwich Theorem Associated with a New Generalized Derivative Operator,” General Mathematics, Vol. 17, No. 4, 2009, pp. 83-95.

[3] A. A. Amer and M. Darus, “A Distortion Theorem for a Certain Class of Bazilevic Function,” International Journal of Mathematical Analysis, Vol. 6, No. 12, 2012, pp. 591-597.

[4] A. A. Amer and M. Darus, “On a Property of a Subclass of Bazilevic Functions,” Missouri Journal of Mathematical Sciences, In Press.

[5] St. Ruscheweyh, “New Criteria for Univalent Functions,” Proceedings of the American Mathematical Society, Vol. 49, No. 1, 1975, pp. 109-115.

[6] G. S. Salagean, “Subclasses of Univalent Functions,” Lecture Notes in Mathematics, Vol. 1013, 1983, pp. 362-372. doi:10.1007/BFb0066543

[7] F. M. Al-Oboudi, “On Univalent Functions Defined by a Generalized Salagean Operator,” International Journal of Mathematics and Mathematical Sciences, Vol. 2004, No. 27, 2004, pp. 1429-1436. doi:10.1155/S0161171204108090

[8] A. W. Goodman, “Univalent Functions and Nonanalytic Curves,” Proceedings of the American Mathematical Society, Vol. 8, No. 3, 1957, pp. 598-601. doi:10.1090/S0002-9939-1957-0086879-9

[9] St. Ruscheweyh, “Neighborhoods of Univalent Functions,” Proceedings of the American Mathematical Society, Vol. 81, No. 4, 1981, pp. 521-527. doi:10.1090/S0002-9939-1981-0601721-6

[10] O. Alintas, H. Irmak and H. M. Srivastava, “Fractional Calculus and Certain Starlike Functions with Negative Coefficietns,” Computers & Mathematics with Applications, Vol. 30, No. 2, 1995, pp. 9-15. doi:10.1016/0898-1221(95)00073-8

[11] O. Alintas, “On a Subclass of Certain Starlike Functions with Negative Coefficients,” Journal of the Mathematical Society of Japan, Vol. 36, 1991, pp. 489-495.

[12] H. Silverman, “Univalent Functions with Negative Coefficients,” Proceedings of the American Mathematical Society, Vol. 51, No. 1, 1975, pp. 109-116. doi:10.1090/S0002-9939-1975-0369678-0

[13] S. K. Chatterjea, “On Starlike Functions,” Journal of Pure Mathematics, Vol. 1, 1981, pp. 23-26.

[14] H. M. Srivastava, S. Owa and S. K. Chatterjea, “A Note on Certain Classes of Starlike Functions,” Rendiconti del Seminario Matematico della Università di Padova, Vol. 77, 1987, pp.115-124.

[15] M. D. Hur and G. H. Oh, “On Certain Class of Analytic Functions with Negative Coefficients,” Pusan Kyongnam Mathematical Journal, Vol. 5, No. 1, 1989, pp. 69-80.

[16] M. Kamali, “Neighborhoods of a New Class of p-Valently Functions with Negative Coefficients,” Mathematical Inequalities & Applications, Vol. 9, No. 4, 2006, pp. 661-670. doi:10.7153/mia-09-59

[17] A. Catas, “Neighborhoods of a Certain Class of Analytic Functions with Negative Coefficients,” Banach Journal of Mathematical Analysis, Vol. 3, No. 1, 2009, pp. 111-121.