Inclusion relations for k-uniformly starlike functions and some linear operator
DOI:
https://doi.org/10.4067/S0716-09172009000200006Keywords:
Starlike, Convex, Linear Operators.Abstract
In this paper, we have established the inclusion relations for k-uniformly starlike functions under the Ls (ai)f(z) operator. These results are also extended to k- uniformly convex functions, close to convex and quasi-convex functions.References
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[18] A. GANGADHARAN, T. N. SHANMUGAM AND H. M. SRIVASTAVA, : Generalized hypergeometric functions associated with k-uniformly convex functions, Comput. Math. Appl., 44, pp. 1515-1526, (2002).
[19] H. M. SRIVASTAVA AND S. OWA, : Some characterization and distortion theorems involving fractional calculus, generalized hypergeometric functions, Hadamard products, linear operators and certain subclasses of analytic functions. Nagoya Math. J., 106, pp. 1-28, (1987).
[20] H. M. SRIVASTAVA AND S. OWA(Eds.), : Univalent functions, Fractional calculus, and their applications, Halsted press(Eills Horwood Limited,Chichester)John Wiley and sons, NewYork,Chichester Brisbane and Toronto, (1989).
[21] H. M. SRIVASTAVA AND S. OWA(Eds.), : Current Topics in Analytic Function Theory, World Scientific Publishing Company, Singapore, New Jersey, London and Hong Kong, (1992).
[22] J. DZIOK AND H. M. SRIVASTAVA, : Classes of analytic functions associated with the generalised hypergeometric function, Appl.Math.Comput., 103, pp. 1-13, (1999).
[23] J. DZIOK AND H. M. SRIVASTAVA, : Some subclasses of analytic functions with fixed argument of coefficients associated with the generalized hypergeometric function, Adv.Stud. Contemp. Math., 5, pp. 115-125, (2002).
[24] S. PONNUSAMY and F. R0NNING, : Duality for Hadamard products applied to certain integral transforms, Comlex Variables:Theory Appl., 32, pp. 263-287, (1997).
[25] Y. C. KIM and H. M. SRIVASTAVA, : Fractional integral and other linear operators associated with the Gaussian hypergeometric function, Complex Variables Theory Appl., 34, pp. 293-312, (1997).
[2] B. C. CARLSON AND S. B. SHAFFER, Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal., 15, pp. 737-745, (1984).
[3] J. DZIOK AND H. M. SRIVASTAVA, Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transform Spec.Funct., 14, pp. 7-18, (2003).
[4] J. DZIOK, R. K. RAINA, AND H. M. SRIVASTAVA, Some classes of analytic functions associated with operators on Hilbert space involving Wright’s generalized hypergeometric function, Proc. Jangjeon Math. Soc., 7, pp. 43-55, (2004).
[5] H. M. SRIVASTAVA AND H. L. MANOCHA, A treatise on generating functions, Wiley/Halsted,New York, (1984).
[6] P. EEINGENBURG, S. S. MILLER, P. T. MOCANU AND M. D. READE, General Inequalities , (BirkhauseverlagBasel), 64 ISNM, pp. 339-348, (1983).
[7] A. W. GOODMAN, On uniformly starlike functions, J. Math. Anal. Appl., 155, pp. 364-370, (1991).
[8] Yu. E. HOHLOV, Operators and operations in the class of univalent functions,Izv. Vyss. Ucebn. Zaved. Mat., 10, pp. 83-89, (1978).
[9] J. -L. LIU, Strongly starlike functions associated with the Dziok-Srivastava operator, Tamkang J. Math., 35, pp. 37-42, (2004).
[10] J. - L. LIU AND H. M. SRIVASTAVA, Classes of meromorphically multivalent functions associated with the generalized hypergeometric function,Math. Comput. Modelling, 38, pp. 21-34, (2004).
[11] J. -L. LIU AND H. M. SRIVASTAVA, Certain properties of the Dziok-Srivastava operator, Appl. Math. Comput., 159, pp. 485-493, (2004).
[12] S. S. MILLER AND P. T. MOCANU, Differential subordination and inequalities in the complex plane, J. Differential Equations, 67, pp. 199-211, (1987).
[13] S. OWA, On the distortion theorem I, Kyungpook Math. J., 18, pp. 53-58, (1978).
[14] S. OWA AND H. M. SRIVASTAVA, Univalent and starlike generalized hypergeometric functions,Cand. J. Math., 39, pp. 1057-1077, (1987).
[15] F. R0NNING, A survey on uniformly convex and uniformly starlike functions, Ann. Univ. Mariae Curie-Sklodowska, 47 (13), pp. 123-134, (1993).
[16] St. RUSCHEWEYH, New criteria for univalent functions, Proc. Amer. Math. Soc., 49, pp. 109-115, (1975).
[17] S. S. MILLER AND P. T. MOCANU, Differential subordination and inequalities in the complex plane, J. Differential Equations, 67, pp. 199-211, (1987).
[18] A. GANGADHARAN, T. N. SHANMUGAM AND H. M. SRIVASTAVA, : Generalized hypergeometric functions associated with k-uniformly convex functions, Comput. Math. Appl., 44, pp. 1515-1526, (2002).
[19] H. M. SRIVASTAVA AND S. OWA, : Some characterization and distortion theorems involving fractional calculus, generalized hypergeometric functions, Hadamard products, linear operators and certain subclasses of analytic functions. Nagoya Math. J., 106, pp. 1-28, (1987).
[20] H. M. SRIVASTAVA AND S. OWA(Eds.), : Univalent functions, Fractional calculus, and their applications, Halsted press(Eills Horwood Limited,Chichester)John Wiley and sons, NewYork,Chichester Brisbane and Toronto, (1989).
[21] H. M. SRIVASTAVA AND S. OWA(Eds.), : Current Topics in Analytic Function Theory, World Scientific Publishing Company, Singapore, New Jersey, London and Hong Kong, (1992).
[22] J. DZIOK AND H. M. SRIVASTAVA, : Classes of analytic functions associated with the generalised hypergeometric function, Appl.Math.Comput., 103, pp. 1-13, (1999).
[23] J. DZIOK AND H. M. SRIVASTAVA, : Some subclasses of analytic functions with fixed argument of coefficients associated with the generalized hypergeometric function, Adv.Stud. Contemp. Math., 5, pp. 115-125, (2002).
[24] S. PONNUSAMY and F. R0NNING, : Duality for Hadamard products applied to certain integral transforms, Comlex Variables:Theory Appl., 32, pp. 263-287, (1997).
[25] Y. C. KIM and H. M. SRIVASTAVA, : Fractional integral and other linear operators associated with the Gaussian hypergeometric function, Complex Variables Theory Appl., 34, pp. 293-312, (1997).
How to Cite
[1]
H. S. Parihar, “Inclusion relations for k-uniformly starlike functions and some linear operator”, Proyecciones (Antofagasta, On line), vol. 28, no. 2, pp. 169-180, 1.
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