Neighborhoods of Certain Classes of Analytic Functions Defined by Normalized Function az^2 J_ϑ'' (z)+bzJ_ϑ' (z)+cJ_ϑ (z)

Year 2020, Volume: 5 Issue: 3, 226 - 232, 30.12.2020

Murat Çağlar , Erhan Deniz , Sercan Kazımoğlu

Abstract

In this paper, we introduce a new subclass of analytic functions in the open unit disk U with negative coefficients defined by normalized of the az^2 J_ϑ^'' (z)+bzJ_ϑ^' (z)+cJ_ϑ (z) function, where J_ϑ (z) is called the Bessel function of the first kind of order ϑ. The object of the present paper is to determine coefficient inequalities, inclusion relations and neighborhoods properties for functions f(z) belonging to this subclass.

Keywords

Analytic function, starlike and convex functions, Bessel function, neighborhoods, coefficient inequality, inclusion relation

References

• [1] Altıntaş, O. and Owa, S. Neighborhoods of certain analytic functions with negative coefficients, Int. J. Math. and Math. Sci. 19, 797-800, 1996.
• [2] Altıntaş, O., Özkan, E. and Srivastava, H. M. Neighborhoods of a class of analytic functions with negative coefficients, Appl. Math. Let. 13, 63-67, 2000.
• [3] Baricz, A., Çağlar, M. and Deniz, E. Starlikeness of bessel functions and their derivatives, Math. Inequal. Appl. 19(2), 439-449, 2016.
• [4] Catas, A. Neighborhoods of a certain class of analytic functions with negative coefficients, Banach J. Math. Anal., 3(1), No. 1, 111-121, 2009.
• [5] Darwish, H. E., Lashin A. Y. and Hassan B. F. Neighborhood properties of generalized Bessel function, Global Journal of Science Frontier Research (F), 15(9), 21-26, 2015.
• [6] Deniz, E. and Orhan, H. Some properties of certain subclasses of analytic functions with negative coefficients by using generalized Ruscheweyh derivative operator, Czechoslovak Math. J., 60(135), 699–713, 2010.
• [7] Elhaddad, S., Aldweby, H. and Darus, M. Neighborhoods of certain classes of analytic functions defined by generalized differential operator involving Mittag-Leffler function, Acta Universitatis Apulensis, No. 55, 1-10, 2018.
• [8] Goodman, A. W. Univalent functions and nonanalytic curves, Proc. Amer. Math. Soc., 8, 598-601, 1957.
• [9] Ismail, M. E. H. and Muldoon, M.E. Bounds for the small real and purely imaginary zeros of Bessel and related functions, Meth. Appl. Anal. 2(1), 1-21 1995.
• [10] Keerthi, B. S., Gangadharan, A. and Srivastava, H. M. Neighborhoods of certain subclasses of analytic functions of complex order with negative coefficients, Math. Comput. Model. 47, 271-277, 2008.
• [11] Mercer, A. McD. The zeros of az^2 J_ϑ^'' (z)+bzJ_ϑ^' (z)+cJ_ϑ (z) as functions of order, Internat. J. Math. Math. Sci., 15, 319-322, 1992.
• [12] Murugusundaramoorthy, G. and Srivastava, H. M. Neighborhoods of certain classes of analytic functions of complex order, J. Inequal. Pure Appl. Math. 5(2), Art. 24. 8 pp., 2004.
• [13] Olver, F. W. J., Lozier, D. W., Boisvert, R. F. and Clark C. W. (Eds.), NIST Handbook of Mathematical Functions, Cambridge Univ. Press, Cambridge, 2010.
• [14] Orhan, H. On neighborhoods of analytic functions defined by using hadamard product, Novi Sad J. Math., 37(1), 17-25, 2007.
• [15] Owa, S., Sekine, T. and Yamakawa, R. On Sakaguchi type functions, Appl. Math. Comput., 187, 356-361, 2007.
• [16] Ruscheweyh, S. Neighborhoods of univalent functions, Proc. Amer. Math. Soc., 81(4), 521-527, 1981.
• [17] Shah, S. M. and Trimble, S. Y. Entire functions with univalent derivatives, J. Math. Anal. Appl., 33, 220-229, 1971.
• [18] Silverman H. Neighborhoods of a classes of analytic function, Far East J. Math. Sci., 3(2), 175-183, 1995.