On Certain Subclass of Starlike Functions with Negative Coefficients Associated with Erdelyi-Kober Integral Operator

Prathiba, S.; Rosy, Thomas

doi:10.2478/gm-2021-0015

Abstract

In this research article, making use of Erdelyi-Kober integral operator, we define a new subclass T^a,c_µ(α, β, γ, A, B) of starlike functions with negative coefficient. Various properties like coefficient estimates, neighbourhood results, integral means, partial sums and subordination results are examined for this class.

References

[1] M. K. Aouf, On subclasses of starlike functions of order α and type β, Tamkang Journal of Mathematics., vol. 21, no. 1, 1990, 41-58.10.5556/j.tkjm.21.1990.4693
Search in Google Scholar Back to article
[2] R. M. EL-Ashwah, M. E. Drbuk, Subordination Properties of p-valent functions defined by linear operators, British J. Math. and Comput. Sci., vol. 4, no. 21, 2016, 3003-3013.10.9734/BJMCS/2014/12121
Search in Google Scholar Back to article
[3] S. D. Bernadi, Convex and starlike univalent functions, Trans. Amer. Math. Soc., vol. 135, 1969, 429-446.10.1090/S0002-9947-1969-0232920-2
Search in Google Scholar Back to article
[4] B. C. Carlson, D. B. Shafer, Starlike and prestarlike Hypergeometric functions, J. Math. Anal., vol. 15, no. 4, 1984, 737-745.10.1137/0515057
Search in Google Scholar Back to article
[5] J. H. Choi, M. Saigo, H. M. Srivastava, Some inclusion properties of a certain family of integral operators, J. Math. Anal. Appl., vol. 276, 2002, 432-445.10.1016/S0022-247X(02)00500-0
Search in Google Scholar Back to article
[6] B. A. Frasin, Partial sums of certain analytic and univalent functions, Acta Math. Acad. Paedagog. Nyhazi., vol. 21, no. 2, 2005, 135-145.
Search in Google Scholar Back to article
[7] B. A. Frasin, G. Murugusundaramoorthy, Partial sums of certain analytic functions, Mathematics, vol. 53, 2011, 131-142.
Search in Google Scholar Back to article
[8] A. W. Goodman, Univalent functions and nonanalytic curves, Proc. Amer. Math. Soc., vol. 8, 1957, 598-601.10.1090/S0002-9939-1957-0086879-9
Search in Google Scholar Back to article
[9] V. P. Gupta, P. K. Jain, Certain classes of univalent functions with negative coefficients, Bull. Austral. Math. Soc., vol. 14, 1976, 409-416.10.1017/S0004972700025326
Search in Google Scholar Back to article
[10] I. B. Jung, Y. C. Kim, H. M. Srivastava, The Hardy space of analytic functions associated with certain parameter families of integral operators, J. Math. Anal. Appl., vol. 176, 1993, 138-147.10.1006/jmaa.1993.1204
Search in Google Scholar Back to article
[11] V. Kiryakova, Generalized Fractional Calculus and Applications, Pitman Research Notes in Mathematics Series, 301, 1994.
Search in Google Scholar Back to article
[12] R. J. Libera, Some classes of regular univalent functions, Proc. Amer. Math. Soc., vol. 16, 1965, 755-758.10.1090/S0002-9939-1965-0178131-2
Search in Google Scholar Back to article
[13] J. E. Littlewood, On inequalities in theory of functions, Proceedings of the London Mathematical Society, vol. 23, 1925, 481-519.10.1112/plms/s2-23.1.481
Search in Google Scholar Back to article
[14] A. E. Livingston, On the radius of univalence of certain analytic functions, Proc. Amer. Math. Soc., vol. 17, 1966, 352-357.10.1090/S0002-9939-1966-0188423-X
Search in Google Scholar Back to article
[15] N. Magesh, M. K. Balaji, R. Sattanathan, Subordination Properties for Certain Subclasses of Prestarlike functions, Punjab University, Journal of Mathematics, vol. 44, 2012, 39-50.
Search in Google Scholar Back to article
[16] G. Murugusundaramoorthy, N. Magesh, On Application of Jung-Kim-Srivastava Integral Oerator to a subclass of starlike functions with negative coefficients, Journal of Computational Analysis and Applications, vol. 9, 2007, 221-232.
Search in Google Scholar Back to article
[17] K. I. Noor, On new classes of integral operators, J. Natural Geometry, vol. 16, 1999, 71-80.
Search in Google Scholar Back to article
[18] K. I. Noor, M. A. Noor, On integral operators, J. Math. Anal. Appl., vol. 238, 1999, 341-352.10.1006/jmaa.1999.6501
Search in Google Scholar Back to article
[19] S. Owa, M. K. Aouf, On subclasses of univalent functions with negative coefficients, Pusan Kyongnam Math. J., vol. 4, 1988, 57-73.
Search in Google Scholar Back to article
[20] T. Rosy, K. G. Subramanian, G. Murugusundaramoorthy, Neighbourhoods and partial sums of starlike functions based on Ruscheweyh derivatives, J. Inequal. Pure Appl. Math., vol. 4, 2003, art. 64.
Search in Google Scholar Back to article
[21] S. Rucheweyh, Neighbourhoods of univalent functions, Proc. Amer. Math. Soc., vol. 81, 1981, 521-527.10.1090/S0002-9939-1981-0601721-6
Search in Google Scholar Back to article
[22] S. Ruscheweyh, New criteria for univalent functions, Proc. Amer. Math. Soc., vol. 49, 1975, 109-115.10.1090/S0002-9939-1975-0367176-1
Search in Google Scholar Back to article
[23] T. Sheil-Small, A note on the partial sums of convex schilicht functions, Bull. London Math. Soc., vol. 2, 1970, 165-168.10.1112/blms/2.2.165
Search in Google Scholar Back to article
[24] H. Silverman, Univalent functions with negative coefficients, Proc.Amer. Math. Soc., vol. 51, 1975, 109-116.10.1090/S0002-9939-1975-0369678-0
Search in Google Scholar Back to article
[25] H. Silverman, Integral means for univalent functions with negative coefficients, Houston Journal of Mathematics, vol. 23, 1997, 169-174.
Search in Google Scholar Back to article
[26] H. Silverman, Partial sums of starlike and convex functions, J.Math. Anal. Appl., vol. 209, no. 1, 1997, 221-227.10.1006/jmaa.1997.5361
Search in Google Scholar Back to article
[27] E. M. Silvia, On partial sums of convex functions of order α, Houston J. Math., vol. 11, no. 3, 1985, 397-404.
Search in Google Scholar Back to article
[28] H. S. Wilf, Subordinating factor sequence for convex maps of the unit circle, Proc. Amer. Math. Soc., vol. 12, 1961, 689-693.10.1090/S0002-9939-1961-0125214-5
Search in Google Scholar Back to article

On Certain Subclass of Starlike Functions with Negative Coefficients Associated with Erdelyi-Kober Integral Operator

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