Certain Subclasses Of Meromorphic Functions With Fixed Second Coefficients Associated With Generalized Polylogarithm Functions
Keywords:
Meromorphic functions, meromorphically starlike functions, meromorphically convex functions.
Abstract
In this paper we introduce and study a subclass GP (α, λ, μ, κ, c) of meromorphic univalent functions which is associated with generalized polylogarithm functions. We obtain coefficient estimates, extreme points, growth and distortion bounds, radii of meromorphically starlikeness and meromorphically convexity for the class GP (α, λ, μ, κ, c) by fixing the second coefficient. Further, it is shown that the class GP (α, λ, μ, κ, c) is closed under convex linear combination.
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References
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[24] S. Sivasubramanian, N. Magesh and M. Darus, A new subclass of meromorphic functions with positive and fixed second coefficients, Tamkang J. Math. 44 (2013), no. 3, 271–278.
[25] V. Srinivas and P. Thirupathi Reddy, Notes on meromorphic functions defined by polylogarithm, Int.J. Math. Trends and Technol., 65 (2019), no. 11, 180 – 186.
[26] H. M. Srivastava, K. R. Alhindi and M. Darus, An investigation into the polylogarithm function and its associated class of meromorphic functions, Majeo Int. J. Sci. Technol., 10(2) (2016), 166 – 174.
[27] P.Thirupathi Reddy, B. Venkateswarlu, Rajkumar N. Ingle and S. Sreelakshmi, On a class of meromorphic functions with positive coefficients involving polylogarithm functions, Libertas Math. (new series) 39 (2019), no. 2, 45–57.
[28] B. A. Uralegaddi, Meromorphically starlike functions with positive and fixed second coefficients, Kyungpook Math. J. 29 (1989), no. 1, 64–68.
[29] B. A. Uralegaddi and M. D. Ganigi, A certain class of meromorphically starlike functions with positive coefficients, Pure Appl. Math. Sci. 26 (1987), no. 1-2, 75–81.
[30] B. A. Uralegaddi and C. Somanatha, Certain differential operators for meromorphic functions, Houston J. Math. 17 (1991), no. 2, 279–284.
[31] B. A. B. A. Uralegaddi and C. Somanatha, New criteria for meromorphic starlike univalent functions, Bull. Austral. Math. Soc. 43 (1991), no. 1, 137–140.
[32] B. Venkateswarlu, P. Thirupathi Reddy and N. Rani, on a certain subclass of meromorphic functions with positive coefficients involving polylogarithm functions, Commun. Optim. Theory 2020 (2020), Article ID 6.
[2] O. Altınta ̧s, H. Irmak and H. M. Srivastava, A family of meromorphically univalent functions with positive coefficients, PanAmer. Math. J. 5 (1995), no. 1, 75–81.
[3] M. K. Aouf, A certain subclass of meromorphically starlike functions with positive coefficients, Rend. Mat. Appl. (7) 9 (1989), no. 2, 225–235.
[4] M. K. Aouf, On a certain class of meromorphic univalent functions with positive coefficients, Rend. Mat. Appl. (7) 11 (1991), no. 2, 209–219.
[5] M. K. Aouf and H. E. Darwish, Certain meromorphically starlike functions with positive and fixed second coefficients, Turkish J. Math. 21 (1997), no. 3, 311–316.
[6] M. K. Aouf and S. B. Joshi, On certain subclasses of meromorphically starlike functions with positive coefficients, Soochow J. Math. 24 (1998), no. 2, 79–90.
[7] M. K. Aouf, N. Magesh, S. Murthy and J. Jothibasu, On certain subclasses of meromorphic functions with positive coefficients, Stud. Univ. Babe ̧s-Bolyai Math. 58 (2013), no. 1, 31–42.
[8] M. Darus, Meromorphic functions with positive coefficients, Int. J. Math. Math. Sci. 2004, no. 5-8, 319–324.
[9] R. M. El-Ashwah, Some subclasses of meromorphically univalent functions, Stud. Univ. Babe ̧s-Bolyai Math. 55 (2010), no. 3, 131–147.
[10] M. R. Ganigi and B. A. Uralegaddi, New criteria for meromorphic univalent functions, Bull. Math. Soc. Sci. Math. R. S. Roumanie (N.S.) 33(81) (1989), no. 1, 9–13.
[11] F. Ghanim and M. Darus, On class of hypergeometric meromorphic functions with fixed second positive coefficients, Gen. Math. 17 (2009), no. 4, 13–28.
[12] A. W. Goodman, Univalent functions and nonanalytic curves, Proc. Amer. Math. Soc. 8 (1957), 598–601.
[13] S. Kavitha, S. Sivasubramanian and K. Muthunagai, A new subclass of meromorphic function with positive coefficients, Bull. Math. Anal. Appl. 2 (2010), no. 3, 109–121.
[14] S. R. Kulkarni and Sou. S. S. Joshi, On a subclass of meromorphic univalent functions with positive coefficients, J. Indian Acad. Math. 24 (2002), no. 1, 197–205.
[15] G. W. Leibniz, Mathematische Schriften. Bd. IV, Herausgegeben von C. I. Gerhardt, Georg Olms Verlagsbuchhandlung, Hildesheim, 1962.
[16] J. E. Littlewood, On Inequalities in the Theory of Functions, Proc. London Math. Soc. (2) 23 (1925), no. 7, 481–519.
[17] N. Magesh, N. B. Gatti and S. Mayilvaganan, On certain subclasses of meromorphic functions with positive and fixed second coefficients involving the Liu-Srivastava linear operator, ISRN Math. Anal. 2012, Art. ID 698307, 11 pp.
[18] N. Magesh and V.Prameela, Partial sums for certain subclasses of meromorphically univalent functions, European J Math. Sci., 1 (2012), no. 1, 88–99.
[19] N. Magesh and V.Prameela, Further properties on certain subclass of meromorphically starlike functions defined by Liu-Srivastava operator, Far East J. Math. Sci., 76(2) (2013) 255-271.
[20] M. L. Mogra, T. R. Reddy and O. P. Juneja, Meromorphic univalent functions with positive coefficients, Bull. Austral. Math. Soc. 32 (1985), no. 2, 161–176.
[21] K. I. Noor, Q. Z. Ahmad and J. Sok ́o l, Applications of the differential operator to a class of meromorphic univalent functions, J. Egyptian Math. Soc. 24 (2016), no. 2, 181–186.
[22] S. Porwal, N. Magesh and A. Khan, A new subclass of hypergeometric meromorphic functions with fixed second positive coefficients, An. Univ. Oradea Fasc. Mat. 22 (2015), no. 1, 33–39.
[23] S. Ruscheweyh, Neighborhoods of univalent functions, Proc. Amer. Math. Soc. 81 (1981), no. 4, 521–527.
[24] S. Sivasubramanian, N. Magesh and M. Darus, A new subclass of meromorphic functions with positive and fixed second coefficients, Tamkang J. Math. 44 (2013), no. 3, 271–278.
[25] V. Srinivas and P. Thirupathi Reddy, Notes on meromorphic functions defined by polylogarithm, Int.J. Math. Trends and Technol., 65 (2019), no. 11, 180 – 186.
[26] H. M. Srivastava, K. R. Alhindi and M. Darus, An investigation into the polylogarithm function and its associated class of meromorphic functions, Majeo Int. J. Sci. Technol., 10(2) (2016), 166 – 174.
[27] P.Thirupathi Reddy, B. Venkateswarlu, Rajkumar N. Ingle and S. Sreelakshmi, On a class of meromorphic functions with positive coefficients involving polylogarithm functions, Libertas Math. (new series) 39 (2019), no. 2, 45–57.
[28] B. A. Uralegaddi, Meromorphically starlike functions with positive and fixed second coefficients, Kyungpook Math. J. 29 (1989), no. 1, 64–68.
[29] B. A. Uralegaddi and M. D. Ganigi, A certain class of meromorphically starlike functions with positive coefficients, Pure Appl. Math. Sci. 26 (1987), no. 1-2, 75–81.
[30] B. A. Uralegaddi and C. Somanatha, Certain differential operators for meromorphic functions, Houston J. Math. 17 (1991), no. 2, 279–284.
[31] B. A. B. A. Uralegaddi and C. Somanatha, New criteria for meromorphic starlike univalent functions, Bull. Austral. Math. Soc. 43 (1991), no. 1, 137–140.
[32] B. Venkateswarlu, P. Thirupathi Reddy and N. Rani, on a certain subclass of meromorphic functions with positive coefficients involving polylogarithm functions, Commun. Optim. Theory 2020 (2020), Article ID 6.
Published
2020-07-21
How to Cite
Swamy, S. R., & Nirmala, J. (2020). Certain Subclasses Of Meromorphic Functions With Fixed Second Coefficients Associated With Generalized Polylogarithm Functions. Journal of Progressive Research in Mathematics, 16(3), 3008-3019. Retrieved from https://scitecresearch.com/journals/index.php/jprm/article/view/1877
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