×

Certain subclass of analytic function associated with a generalization of \(q\)-Salagean operator with negative coefficients. (English) Zbl 1474.30092

Summary: In this paper, we study different properties for the new class \(TY^\lambda_q (n, \alpha, \beta, \gamma)\) of analytic starlike and convex functions associated with a generalization of \(q\)-Salagean operator.

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)

References:

[1] F. M. AL-Oboudi, On univalent functions defined by a generalized Sȃlȃgean operator, Inter-nat. J. Math. Math. Sci., 27, 1429-1436, 2004. · Zbl 1072.30009
[2] M. H. Annby and Z. S. Mansour, q−Fractional Calculus Equations, Lecture Notes in Math., 2056, Springer-Verlag Berlin Heidelberg, 2012. · Zbl 1267.26001
[3] M. K. Aouf, Neighborhoods of certain classes of analytic functions with negative coefficients, Internet. J. Math. Sci., 2006, Article ID38258, 1-6, 2006. · Zbl 1118.30006
[4] M. K. Aouf, Subordination properties for a certain class of analytic functions defined by Sȃlȃgeȃn operator, Appl. Math. Letters, 22, 1581-1585, 2009. · Zbl 1171.30302
[5] M. K. Aouf, A subclass of uniformly convex functions with negative coefficients, Math. Tome 52, 75 (2), 99-111, 2010. · Zbl 1224.30026
[6] M. K. Aouf and N. E. Cho, On a certain subclass of analytic functions with negative coeffi-cients, Tr. J. Math., 22, 15-32, 1998. · Zbl 0910.30011
[7] M. K. Aouf, H. E. Darwish and G. S. Sȃlȃgeȃn, On a generalization of starlike functions with negative coefficients, Math. Tome 43, 66 (1), 3-10, 2001. · Zbl 1097.30502
[8] M. K. Aouf and A. O. Mostafa, Some properties of a subclass of uniformly convex functions with negative coefficients, Demonstratio Math., 41 (2), 353-370, 2008. · Zbl 1159.30307
[9] M. K. Aouf, A. O. Mostafa and F. Y. AL-Quhali, Properties for class of β−uniformly univalent functions defined by type q−difference operator, Int. J. Open Problems of Complex Analysis, 11 (2), 1-16, 2019.
[10] M. K. Aouf, A. O. Mostafa, A. Y. Lashin and B. M. Munassar, Partial sums for a certain subclass of meromorphic univalent functions, Sarajevo J. Math., 10 (23), 161-169, 2014. · Zbl 1318.30019
[11] M. K. Aouf, A. Shamandy, A. O. Mostafa and E. A. Adwan, Partial sums of certain of analytic functions defined by Dziok-Srivastava operator, Acta Univ. Apulensis, 30, 65-76, 2012. · Zbl 1289.30045
[12] M. K. Aouf and T. M. Seoudy, Convolution properties for classes of bounded analytic func-tions with complex order defined by q-derivative operator, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math., 113 (2), 1279-1288, 2019. · Zbl 1421.30014
[13] M. K. Aouf, A. Shamandy, A. O. Mostafa and F. El-Emam, Subordination results associated with β− uniformly convex and starlike functions, Pro. Pakistan Acad. Sci., 46 (2), 97-101, 2009.
[14] A. Aral, V. Gupta, and R. P. Agarwal, Applications of q-Calculus in Operator Theory, Springer, New York, USA, 2013. · Zbl 1273.41001
[15] B. A. Frasin, Partial sums of certain analytic and univalent functions, Acta Math. Acad. Paed. Nyir, 21, 135-145, 2005. · Zbl 1092.30019
[16] B. A. Frasin and G. Murugusundaramoorthy, Partial sums of certain analytic and univalent functions, Mathematica, Tome., 53 (75) (2), 131-142, 2011. · Zbl 1265.30057
[17] G. Gasper and M. Rahman, Basic Hypergeometric Series, Combridge Univ. Press, Cambri-didge, U. K., 1990. · Zbl 0695.33001
[18] M. Govindaraj and S. Sivasubramanian, On a class of analytic function related to conic domains involving q−calculus, Analysis Math., 43 (3) (5), 475-487, 2017. · Zbl 1399.30047
[19] F. H. Jackson, On q-functions and a certain difference operator, Trans. Royal. Soc. Edinburgh, 46, 253-281, 1908.
[20] J. E. Littlewood, On inequalities in theory of functions, Proc. London Math. Soc., 23, 481-519, 1925. · JFM 51.0247.03
[21] A. O. Mostafa, On partial sums of certain analytic functions, Demonstratio Math., 41 (4), 779-788, 2008. · Zbl 1160.30322
[22] M. S. Robertson, On the theory of univalent functions, Ann. Math., 37, 374-408, 1936. · JFM 62.0373.05
[23] T. Rosy and G. Murugusundaramoorthy, Fractional calculus and their applications to certain subclass of uniformly convex functions, Far East J. Math. Sci., (FJMS), 115 (2), 231-242, 2004. · Zbl 1073.30012
[24] T. Rosy, K. G. Subramanian and G. Murugusundaramoorthy, Neighborhoods and partial sums of starlike functions based on Ruscheweyeh derivatives, J. Ineq. Pure Appl. Math., 64 (4), Art., 4, 1-8, 2003. · Zbl 1054.30014
[25] G. Sȃlȃgean, Subclasses of univalent functions, Lect. Notes in Math., (SpringerVerlag), 1013, 362-372, 1983. · Zbl 0531.30009
[26] T. M. Seoudy and M. K. Aouf, Convolution properties for certain classes of analytic functions defined by q-derivative operator, Abstr. Appl. Anal. 2014, Article ID 846719, 1-7, 2014. · Zbl 1474.30117
[27] T. M. Seoudy and M. K. Aouf, Coefficient estimates of new classes of q-starlike and q-convex functions of complex order, J. Math. Ineq., 10 (1), 135-145, 2016. · Zbl 1333.30027
[28] T. Sheil-Small. A note on partial sums of convex schlicht functions, Bull. London Math, Soc., 2, 165-168, 1970. · Zbl 0217.09701
[29] H. Silverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc., 51, 109-116, 1975. · Zbl 0311.30007
[30] H. Silverman, A survey with open problems on univalent functions whose coefficients are negative, Rocky Mt. J. Math., 21, 1099-1125, 1991. · Zbl 0766.30011
[31] H. Silverman, Integral means for univalent functions with negative coefficients, Houston J. Math., 23, 169-174, 1997. · Zbl 0889.30010
[32] H. Silverman, Partial sums of starlike and convex functions, J. Math. Appl., 209, 221-227, 1997. · Zbl 0894.30010
[33] A. Schild and H. Silverman, Convolution of univalent functions with negative coefficients, Ann. Univ. Mariae Curie-Sklodowska sect. A, 29, 99-106, 1975. · Zbl 0363.30018
[34] H. M. Srivastava and A. O. Mostafa, M. K. Aouf and H. M. Zayed, Basic and fractional q-calculus and associated Fekete-Szegö problem for p-valently q-starlike functions and p-valently q-convex functions of complex order, Miskolc Math. Notes 20 (1), 489-509, 2019. · Zbl 1438.26015
[35] H. M. Zayed and M. K. Aouf, Subclasses of analytic functions of complex order associated with q-Mittag Leffler function, J. Egyptian Math. Soc., 26 (2), 278-286, 2018. · Zbl 1435.30071
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.