[11] Brannan, D. A. and Kirwan, W. E., On some classes of bounded univalent functions, J. London Math. Soc., 2(1)(1969), [12] Brickman, L.

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1 Bibliography [1] Aghalary, R., Ali, R. M., Joshi, S. B. and Ravichandran, V., Inequalities for analytic functions defined by certain linear operators, Int. J. Math. Sci., 4(2005), [2] Ahuja, O. P. and Silverman, H., Classes of functions whose derivatives have positive real part, J. Math. Anal. Appl., 138 (2) (1989), [3] Al-Amiri, H. S. and Reade, M. O., On a linear combination of some expressions in the theory of univalent functions, Monatshefto für mathematik, 80(1975), [4] Ali, R. M., Badghaish, A. O. and Ravichandran, V., Subordination for higherorder derivatives of multivalent functions, Journal of Inequalities and Applications, 2008, Article ID , 12 pages. [5] Ali, R. M., Ponnusamy, S. and Singh, V., Starlikeness of functions satisfying a differential inequality, Ann. Polon. Math., 61(2)(1995), [6] Ali, R. M., Ravichandran, V., Khan, M. H. and Subramanian, K. G., Differential sandwich theorems for certain analytic functions, Far East J. Math. Sci., 15(1)(2004), [7] Ali, R. M., Ravichandran, V. and Lee, S. K., Subclasses of multivalent starlike and convex functions, Bulletin of the Belgian Mathematical Society - Simon Stevin, to appear. [8] Ali, R. M., Ravichandran, V. and Seenivasagan, N., Differential subordination and superordination on Schwarzian derivatives, J. Inequal. Appl., 2008, Article ID , 18 pages. [9] Bieberbach, L., Über die koeffizienten derjenigen Potenzreihen, Welche eine schlichte Abbildung des Einheitskreises vermitteln, S.B.Preuss Akad. Wiss., 138 (1916), [10] Branges, L. de, A proof of the Bieberbach conjecture, Acta Math., 154(1985),

2 [11] Brannan, D. A. and Kirwan, W. E., On some classes of bounded univalent functions, J. London Math. Soc., 2(1)(1969), [12] Brickman, L., φ-like analytic functions I, Bull. Amer. Math. Soc., 79(1973), [13] Bulboaca, T., Classes of first-order differential superordinations, Demonstratio Mathematica, 35(2)(2002), [14], A class of superordination-preserving integral operators, Indagationes Mathematicae, 13(3)(2002), [15], Generalized Briot-Bouquet differential subordinations and superordinations, Rev. Roumaine Math. Pures Appl., 47(5-6)(2002), [16], Differential subordinations and superordinations: Recent results, House of science Book Publ., Cluj-Napoca, [17] Bulboaca, T. and Tuneski, N., New criteria for starlikeness and strongly starlikeness, Mathematica (Cluj), 43(66)(2001), [18] Carlson, B. C. and Shaffer, D. B., Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal., 15(4)(1984), [19] Cho, N. E. and Kim, J., On a sufficient condition and an angular estimation for φ-like functions, Taiwan. J. Math., 2(4)(1998), [20] Cho, N. E. and Kim, T. H., Multiplier transformations and strongly close-toconvex functions, Bull. Korean Math. Soc., 40(2003), [21] Cho, N. E. and Srivastava, H. M., Argument estimates of certain analytic functions defined by a class of multiplier transformations, Math. Comput. Modelling, 37(2003), [22] Darus, M. and Thomas, D. K., α - logarithmatically convex functions, Indian J.pure and appl. Math. 29(10)(1984), [23] Duren, P. L., Univalent functions, Springer Verlag, N.Y., Berlin, Heidelberg, Tokyo (1983). [24] Eenigenburg, P. J., Miller, S. S., Mocanu, P. T. and Reade, M. O., On a Briot-Bouquet differential subordination, General Inequalities, 3, International Series of Numerical Mathematics, Vol. 64, Birkhäuser Verlag, Basel (1983), [25] Fukui, S., On α-convex functions of order β, Int. J. Math. & Math. Sci., 20, 4(1997),

3 [26] Goodman, A. W., Univalent functions, Volume 1, Mariner Publishing Co., Tampa, Florida, (1983). [27] Graham, I. and Kohr, G., Geometric function theory in one and higher dimensions, Marcel Dekker Inc., New York (2003). [28] Gupta, S., Singh, S. and Singh, S., A criterion of φ-like functions, General Mathematics, 15(4)(2007), MR (2009d:30024) [29] Hallenbeck, D. J. and Ruscheweyh, St., Subordination by convex functions, Proc. Amer. Math. Soc., 52(1975), [30] Hayman, W. K., Multivalent Functions, Cambridge University Press, [31] Ibrahim, R. W. and Darus, M., Subordination and superordination for univalent solutions for fractional differential equations, J. Math. Anal. Appl., 245(2008), [32] Irmak, H. and Cho, N. E., A differential operator and its applications to certain multivalently analytic functions, Hacettepe Journal of Mathematics and Statistics, 36(1)(2007), pp [33] Irmak, H. and Raina, R. K., The starlikeness and convexity of multivalent functions involving certain inequalities, Revista Matemática Complutense, 16(2)(2003), [34] Jack, I.S., Functions starlike and convex of order α, J. London Math. Soc., 3(1971), [35] Kanas, S., Lecko, A. and Stankiewicz, J., Differential subordinations and geometric means, Complex Variables, 28(1996), [36] Kaplan, W., Close-to-convex schlicht functions, Michigan Math. J., 1(1952), [37] Kiliç, Ö. Ö., Sufficient conditions for subordination of multivalent functions, Journal of Inequalities and Applications, 2008, Article ID , 8 pages. [38] Koebe, P., Über die Uniformisierung beliebiger analytischer kurven, Nachr. Akad. Wiss. Göttingen, Math-Phys. Kl., (1907), [39] Kufarev, P. P., On one parameter families of analytic functions (Russian), Mat. Sb., 13(1943), [40] Kumar, S., Ravichandran, V. and Taneja, H. C., Classes of multivalent functions defined by Dziok-Srivastava linear operators, Kyungpook Math. J., 46(2006),

4 [41] Lewandowski, Z., Miller S. S. and Zlotkiewicz, E., Generating functions for some classes of univalent functions, Proc. Amer. Math. Soc., 56(1976), [42] Li, J. and Owa, S., Properties of the Sălăgean operator, Georgian Math. J., 5(4)(1998), [43], Sufficient conditions for starlikeness, Indian J. Pure Appl. Math., 33(2002), [44] Lindelöf, E., Mémoire sur certaines inéqalités dans la théorie des fonctions monogénes et sur quelques propriétés nouvelles de ces fonctions dans le voisinage d un point singulier essentiel, Acta Soc. Sci. Fenn., 35(7)(1909), [45] Littlewood, J. E., On inequalities in the theory of functions, Proc. London Math. Soc., 23(1925), [46], Lectures on the theory of functions, Oxford University Press, London (1944). [47] Löewner, K., Untersuchungen über schlichte konforme abbildungen des einheitskreises, Math. Ann., 89(1923), [48] Marx, A., Untersuchungen über schlichte abbildungen, Math. Ann., 107(1932/33), [49] Miller, S. S., Differential inequalities and carathéodory functions, Bull. Amer. Math. Soc., 81(1975), [50] Miller, S. S. and Mocanu, P. T., Second-order differential inequalities in the complex plane, J. Math. Anal. Appl., 65(1978), [51], Differential subordinations and univalent functions, Michigan Math. J., 28(1981), [52], On some classes of first order differential subordinations, Michigan Math. J., 32(1985), [53], Univalent solutions of Briot-Bouquet differential equations, J. Diff. Eqns., 56(3)(1985), [54], Differential subordinations and inequalities in the complex plane, J. Diff. Eqns., 67(1987), [55], A special differential subordination and its application to univalency conditions, Current topics in analytic function theory, World Scientific, Singapore, London, (1992),

5 [56], Briot-Bouquet differential equations and differential subordinations, Complex Variables, 33(1997), [57], Differential subordinations: Theory and applications, Marcel Dekker, New York and Basel, [58], Subordinants of differential superordinations, Complex Variables, 48(10)(2003), [59], Briot-Bouquet differential superordinations and sandwich theorems, J. Math. Anal. Appl., 329(1)(2007), [60] Miller, S. S., Mocanu, P. T. and Reade, M. O., All α- convex functions are univalent and starlike, Proc. Amer. Math. Soc., 37(1973), [61], Bazilevic functions and generalized convexity, Rev. Roumaine Math. Pures Appl., 19(1974), [62] Mocanu, P. T., Une propriété de convexité generalisée dans la théorie da la représentation conforme, Mathematica (Cluj), 11,34(1969), [63], Alpha-convex integral operators and strongly starlike functions, Studia Univ. Babes-Bolyai Math., 34,2(1989), [64], Two simple sufficient conditions for starlikeness, Mathematica (Cluj), 34(57), 2(1992), [65], Some simple criteria for starlikeness and convexity, Libertas Mathematica, 13(1993), [66] Mocanu, P. T. and Oros, Gh., Sufficient conditions for starlikeness, Studia Univ. Babes-Bolyai, Math., 43(1)(1998), [67] Mocanu, P. T. and Serb, I., A sharp simple criterion for a subclass of starlike functions, Complex Variables, 32(1997), [68] Muhammet, K., A criterion for p-valently starlikeness, J. Inequal. Pure Appl. Math., 4(2)(2003), Art. 36, 1-5. [69] Nehari, Z., Conformal mapping, Mc. Graw-Hill Book Comp., 1952 (Dover Publ. Inc., 1975). [70] Noshiro, K., On the theory of schlicht functions, J. Fac. Sci., Hokkaido Univ., 2( ), [71] Nunokawa, M., On certain multivalent functions, Math. Japon., 36(1991),

6 [72], A certain class of starlike functions, Current Topics in Analytic Function Theory, Srivastava, H. M. and Owa, S.(Eds.), Singapore, New Jersey, London, Hong Kong, 1992, p [73] Nunokawa, M., Cho, N. E., Kwon, O. S., Owa, S. and Saitoh, H., Differential inequalities for certain analytic functions, Comput. Math. Appl., 56(2008), [74] Nunokawa, M., Owa, S., Saitoh, H. and Ahuja., O. P., On the quotient of convex and starlike factors defined by Silverman, Mathematica, Tome, 45(68)(2003), [75] Obradovi c, M., Joshi, S. B. and Jovanovic, I., On certain sufficient conditions for starlikeness and convexity, Indian J. Pure Appl. Math., 29(3)(1998), [76] Obradovi c, M. and Owa, S., A criterion for Starlikeness, Math. Nachr., 140(1989), [77] Obradovi c, M., Ponnusamy, S., Singh, V. and Vasundhra, P., Differential inequalities and criteria for starlike and univalent functions, Rocky Mountain J. Math., 36(1)(2006), [78] Obradovi c, M. and Tuneski, N., On the starlike criteria defined by Silverman, Zeszyty Nauk. Politech. Rzeszowskiej. Mat., 181(24)(2000) [79] Owa, S., Nishiwaki, J. and Niwa, N., Subordinations for certain analytic functions, Int. J. Open Problems Compt. Math., 1(2)(2008), [80] Owa, S., Nunokawa, M., Saitoh, H. and Srivastava, H. M., Close-toconvexity, starlikeness and convexity of certain analytic functions, Appl. Math. Letters., 15(2002), [81] Owa, S., Obradovi c, M. and Lee, S. K., Notes on a certain subclass of analytic functions introduced by Sălăgean, Bull. Korean Math. Soc., 23(1986), [82] Owa, S., Shen, C.Y. and Obradovi c, M., Certain subclasses of analytic functions, Tamkang J. Math., 20(1989), [83] Padmanabhan, K. S., On sufficient conditions for starlikeness, Indian J.Pure appl. Math., 32,4(2001), [84] Patel, J. and Cho, N. E., On certain sufficient conditions for close-toconvexity, Appl. Math. Comput., 187(2007), [85] Pommerenke, Ch., Univalent functions, Vandenhoeck and Ruprecht, Göttingen, (1975). 122

7 [86] Ponnusamy, S., Pòlya-Schoenberg conjecture for carathèodory functions, J. London Math. Soc., 51(2)(1995), [87], New sufficient conditions for starlike and univalent functions, Soochow J. Math., 21(2)(1995), [88] Ponnusamy, S. and Singh, V., Criteria for strongly starlike functions, Complex Variables: Theory and Appl., 34(1997), [89] Ravichandran, V., Certain applications of first order differential subordination, Far East J. Math. Sci., 12(1)(2004), [90] Ravichandran, V. and Darus, M., On a criteria for starlikeness, Int. Math. J., 4(2)(2003), [91] Ravichandran, V. and Darus, M., On a criteria for starlikeness, J. Anal. Appl., 2(1)(2004), [92] Ravichandran, V., Magesh, N. and Rajalakshmi, R., On certain applications of differential subordinations for φ-like functions, Tamkang J. Math., 36(2)(2005) [93] Ravichandran, V., Selvaraj, C. and Rajalakshmi, R., Sufficient conditions for starlike functions of order α, J. Inequal. Pure and Appl. Math., 3(5)(2002) Art. 81, 1-6. [94] Robertson, M. S., On the theory of univalent functions, Ann. Math., 37(1936), [95], Certain classes of starlike functions, Michigan Math. J., 32(1985), [96] Rogosinski, W., On subordinate functions, Proc. Cambridge Philos. Soc., 35(1939), [97], On the coefficients of subordinate functions, Proc. London Math. Soc., 48(1943), [98] Ruscheweyh, St., A subordination theorem for φ-like functions, J. London Math. Soc., 2(13)(1976), [99] Ruscheweyh, St. and Singh, V., On a Briot-Bouquet equation related to univalent functions, Rev. Roumaine Math. Pures Appl., 24(1979), [100] Ruscheweyh, St. and Stankiewicz, J., Subordination under convex univalent functions, Bull. Polish Acad. Sci. Math., 33(1985), [101] Sălăgean, G. S., Subclasses of univalent functions, Lecture Notes in Math., 1013, , Springer-Verlag, Heidelberg,

8 [102] Sakaguchi, K., On a certain univalent mapping, J. Math. Soc. Japan, 2(1959), [103] Shanmugam, T. N., Sivasubramanian, S. and Darus, M., Subordination and superordination results for φ-like functions, J. Inequal. Pure and Appl. Math., 8(1)(2007), 1-6. [104] Shanmugam, T. N., Sivasubramanian, S. and Silverman, H., Differential sandwich theorems for some classes of analytic functions, Australian J. Math. Anal. Appl., 3(1)(2005), Article 8, pp [105], On sandwich theorems for some classes of analytic functions, Int. J. Math. & Math. Sci.,(2006), Article ID 29684, pp [106], On sandwich theorems for certain subclasses of analytic functions involving Carlson-Shaffer operator, J. Korean Math. Soc., 45(3)(2008), pp [107] Silverman, H., Convex and starlike criteria, Int. J. Math. & Math. Sci., 22(1)(1999), [108] Singh, S. and Gupta, S., Some applications of a first order differential subordination, J. Inequal. Pure and Appl. Math. 5(3)(2004), Art. 78, [109], On certain differential subordination and its dominants, Bull. Belg. Math. Soc. Simon Stevin 12(2005), [110] Singh, S., Gupta, S. and Singh, S., On a problem of univalence of functions satisfying a differential inequality, Math. Inequal. Appl., 10(1)(2007), MR (2007i:30039) [111], On a bounded subclass of certain analytic functions satisfying a differential inequality, J. Math. Inequal., 2(1)(2008), MR (2009m:30030) [112], On a class of multivalent functions defined by a multiplier transformation, Matematicki Vesnik, 60(2008), MR (2009f:30039) [113], On starlikeness and convexity of analytic functions satisfying a differential inequality, J. Inequal. Pure and Appl. Math., 9(3)(2008), Art. 81, 1-7. MR (2009h:30024) [114], On a problem in the theory of univalent functions, General Mathematics, 17(3)(2009), MR (2011e:30054) [115], An extension of the region of variability of a subclass of univalent functions, J. Inequal. Pure and Appl. Math., 10(4)(2009), Art. 113, 1-7. MR (2011a:30050) 124

9 [116], On certain results of differential subordination and superordination, Commun. Math. Anal., 6(2)(2009), MR (2010j:30032) [117], A sandwich-type theorem with applications to univalent functions, Int. J. Math. and Compt. Sci., 5(4)(2009), [118], Differential subordination and superordination theorems for certain analytic functions, General Mathematics, 18(2)(2010), MR [119], Certain applications of differential subordination to analytic functions, Int. J. Open Problems Complex Analysis, 2(1)(2010), [120], Starlikeness of analytic maps satisfying a differential inequality, General Mathematics, 18(3)(2010), MR [121], A first order differential subordination and its applications, Int. J. Open Problems Complex Analysis, 2(2)(2010), [122] Singh, S., Gupta, S. and Singh, V., An application of differential subordination, Math. Sci. Res. J., 8(9)(2004) [123] Singh, V., On a class of univalent functions, Int. J. Math. & Math. Sci. 23(12)(2000), [124], On some problems of Mocanu type, Indian J. Pure Appl. Math. 32(12)(2001), pp [125], On some criteria for univalence and starlikeness, Indian J. Pure. Appl. Math. 34(4)(2003), [126] Singh, V., Singh, S. and Gupta, S., A problem in the theory of univalent functions, Integral Transforms and Special Functions, 16(2)(2005), [127] Singh, V. and Tuneski, N., On a criteria for starlikeness and convexity of analytic functions, Acta Math. Sci. 24(B4)(2004), [128] Srivastava, H. M. and Attiya, A. A., Some applications of differential subordination, Appl. Math. Letters, 20(2007) [129] Stankiewicz, J., Some remarks concerning starlike functions, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phy., 18(1970), [130] Strohhäcker, E., Beitrage zur theorie der schlichten funktionen, Math. Z., 37(1933),

10 [131] Tuneski, N., On certain sufficient conditions for starlikeness, Int. J. Math. & Math. Sci., 23(8)(2000), [132], On some simple sufficient conditions for univalence, Mathematica Bohemica, 126(2001), [133], On a criteria for starlikeness of analytic functions, Integral Trans. Special Functions, 14(3)(2003), [134], On the quotient of the representations of convexity and starlikeness, Math. Nachr., (1)(2003), [135], Some results on starlike and convex functions, Applicable Analysis and Discrete Math., 1(2007), [136] Tuneski, N. and Irmak, H., Starlikeness and convexity of a class of analytic functions, Int. J. Math. & Math. Sci., (2006), Article ID 38089, pp [137] Uralegaddi, B. A. and Somanatha, C., Certain classes of univalent functions, in Current Topics in Analytic Function Theory, H. M. Srivastava and S. Owa (ed.), World Scientific, Singapore, (1992), [138] Warchawski, S. E., On the higher derivatives at the boundary in conformal mappings, Trans. Amer. Math. Soc., 38(1935),

11 List of Publications 1. Singh, S., Gupta, S. and Singh, S., On a problem of univalence of functions satisfying a differential inequality, Math. Inequal. Appl., 10(1)(2007), MR (2007i:30039) 2., A criterion of φ-like functions, General Mathematics, 15(4)(2007), MR (2009d:30024) 3., On a bounded subclass of certain analytic functions satisfying a differential inequality, J. Math. Inequal., 2(1)(2008), MR (2009m:30030) 4., On a class of multivalent functions defined by a multiplier transformation, Matematicki Vesnik, 60(2008), MR (2009f:30039) 5., On starlikeness and convexity of analytic functions satisfying a differential inequality, J. Inequal. Pure and Appl. Math., 9(3)(2008), Art. 81, 1-7. MR (2009h:30024) 6., On a problem in the theory of univalent functions, General Mathematics, 17(3)(2009), MR (2011e:30054) 7., An extension of the region of variability of a subclass of univalent functions, J. Inequal. Pure and Appl. Math., 10(4)(2009), Art. 113, 1-7. MR (2011a:30050) 8., On certain results of differential subordination and superordination, Commun. Math. Anal., 6(2)(2009), MR (2010j:30032) 9., A sandwich-type theorem with applications to univalent functions, Int. J. Math. and Compt. Sci., 5(4)(2009), , Differential subordination and superordination theorems for certain analytic functions, General Mathematics, 18(2)(2010), MR , Certain applications of differential subordination to analytic functions, Int. J. Open Problems Complex Analysis, 2(1)(2010), , Starlikeness of analytic maps satisfying a differential inequality, General Mathematics, 18(3)(2010), MR , A first order differential subordination and its applications, Int. J. Open Problems Complex Analysis, 2(2)(2010),

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