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 Section Mathematics Title On a subclass of univalent functions with negative coefficients defined by a linear operator Author(-s) Juma A.R.a, Abdul-Hussein M.Sh.b, Hani M.F.b Affiliations University of Anbara, University of Mustansiriyahb Abstract The present paper introduces and studies the subclass $A_{n} (m,\beta,p,q,\lambda)$ of univalent functions with negative coefficients defined by new linear operator $J^\lambda$ in the open unit disk $\mathcal{U}=\{z \in \mathbb{C}: |z| < 1\}$. The main task is to investigate several properties such as coefficient estimates, distortion theorems, closure theorems. Neighborhood and radii of starlikeness, convexity and close-to-convexity of functions belonging to the class $A_{n} (m,\beta,p,q,\lambda)$ are studied. Keywords analytic univalent function, Hadamard product, Ruscheweyh derivative, distortion theorems, closure theorems UDC 517.53 MSC 30C45 DOI 10.20537/vm150302 Received 29 April 2015 Language English Citation Juma A.R., Abdul-Hussein M.Sh., Hani M.F. On a subclass of univalent functions with negative coefficients defined by a linear operator, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2015, vol. 25, issue 3, pp. 306-317. References Aghalary R., Kulkarni S. Some theorem on univalent functions, J. India Acad. Math., 2002, vol. 24, no. 1, pp. 81-93. Aouf M.K. Neighborhoods of certain class of analytic functions with negative coefficients, International Journal of Mathematics and Mathematical Sciences, 2006, Article ID 38258, 6 p. http://dx.doi.org/10.1155/IJMMS/2006/38258 Goodman A.W. Univalent functions and nonanalytic curves, Proc. Amer. Math. Soc., 1957, vol. 8, no. 3, pp. 598-601. Juma A.R.S., Zirar H. Properties of a subclass of $p$-valent functions defined by new operator $V_p$$\lambda$ , An. Univ. Oradea, Fasc. Mat., 2014, vol. 21, no. 1, pp. 73-82. Juma A.R.S., Kulkarni S.R. On univalent functions with negative coefficients by using generalized Salagean operator, Filomat, 2007, vol. 21, no. 2, pp. 173-184. http://dx.doi.org/10.2298/FIL0702173J Khairnar S.M., More M. Certain family of analytic and univalent functions with normalized conditions, Acta Math. Acad. Paedagog. Nyházi. (N.S.), 2008, vol. 24, no. 3, pp. 333-344. Kulkarni S.R. Some problems connected with univalent functions, Ph.D Thesis, 1981, Shivaji University, Kolhapur. Kumar V., Shukla S.L. Multivalent functions defined by Ruscheweyh derivatives. II, Indian J. Pure Appl. Math., 1984, vol. 15, pp. 1228-1238. Lakshminarasimhan T.V. On subclasses of functions starlike in the unit disc, J. Indian Math. Soc., New Ser., 1977, vol. 41, pp. 233-243. Orhan H., Kamali M. Neighborhoods of a class of analytic functions with negative coefficients, Acta Math. Acad. Paedagog. Nyházi. (N.S.), 2005, vol. 21, no. 1, pp. 55-61. Patel J., Cho N.E., Srivastava H.M. Certain subclasses of multivalent functions associated with a family of linear operators, Mathematical and Computer Modelling, 2006, vol. 43, no. 3-4, pp. 320-338. Raina R.K., Srivastava H.M. Inclusion and neighborhood properties of some analytic and multivalent functions, JIPAM, J. Inequal. Pure Appl. Math., 2006, vol. 7, no. 1, paper no. 5, 6 p. Ruscheweyh S. New criteria for univalent functions, Proc. Amer. Math. Soc., 1975, vol. 49, no. 1, pp. 109-115. Ruscheweyh S. Neighborhoods of univalent functions, Proc. Amer. Math. Soc., 1981, vol. 81, no. 4, pp. 521-527. Silverman H. Univalent functions with negative coefficents, Proc. Amer. Math. Soc., 1975, vol. 51, no. 1, pp. 109-116. Full text