Properties On A New Comprehensive Family Of Holomorphic Functions Associated With Ruscheweyh Derivative and Generalized Multiplier Transformations
Keywords:
Holomorphic function, Ruscheweyh derivative, Multiplier transformatiion, Coefficient inequalities.
Abstract
In the present paper, a new comprehensive family of holomorphic functions, which includes various new subfamilies of holomorphic functions as well as some very well-known ones, is introduced. Sharp results concerning coefficient inequalities and distortion bounds of functions belonging to these families are determined. Furthermore, functions with negative coefficients belonging to these families are also investigated.
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References
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S R SWAMY, MASLINA DARUS, Y SAILAJA: PROPERTIES ON A NEW COMPREHENSIVE FAMILY OF ... 9
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operator, American International Journal of Research in Science, Technology, Engineering and Mathematics,
11(1)(2015),65-71.
[11] S. R. Swamy, Ruscheweyh derivative and a new generalized Multiplier differential operator, Annals of pure and Applied Mathematics, (10)(2)(2015),229-238.
[12] S. R. Swamy, Inclusion properties of certain subclasses of analytic functions, Int. Math. Forum, 7(36) (2012),
1751-1760.
27(2004), 1429-1436.
[2] S. S. Bhoosnurmath and S. R. Swamy, On certain classes of analytic functions, Soochow J. Math., 20 (1) (1994),
1-9.
[3] A. Catas, On certain class of p-valent functions defined by new multiplier transformations, Proceedings book of an international symposium on geometric function theory and applications, August, 20-24, (2007), TC Istanbul
Kultur Univ., Turkey, 241-250.
[4] M. Darus and R. Ibrahim, New classes containing generalization of differential operator, Applied Math. Sci., 3
(51) (2009) , 2507-2515.
[5] D. O. Makinde, J. O. Hamzat and A. M Gbolagade, A generalized multiplier transformation on univalent integral operator, J. Contemporary Appl. Math.,9(1)(2019),31-38.
[6] St. Ruscheweyh, New criteria for univalent functions, Proc. Amer. Math. Soc., 49(1975), 109-115.
[7] G. St. S˘al˘agean, Subclasses of univalent functions, Proc. Fifth Rou. Fin. Semin. Buch. Complex Anal., Lect. notes in Math., Springer -Verlag, Berlin, 1013(1983), 362-372.
[8] H. Silverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc., 51(1) (1975), 109-116.
S R SWAMY, MASLINA DARUS, Y SAILAJA: PROPERTIES ON A NEW COMPREHENSIVE FAMILY OF ... 9
[9] S. R. Swamy, On analytic functions defined by Ruscheweyh derivative and a new generalized multiplier differential operator, Int. J. Math. Arch., 6(7) (2015), 168-177.
[10] S. R. Swamy, New classes containing Ruscheweyh derivative and a new generalized multiplier differential
operator, American International Journal of Research in Science, Technology, Engineering and Mathematics,
11(1)(2015),65-71.
[11] S. R. Swamy, Ruscheweyh derivative and a new generalized Multiplier differential operator, Annals of pure and Applied Mathematics, (10)(2)(2015),229-238.
[12] S. R. Swamy, Inclusion properties of certain subclasses of analytic functions, Int. Math. Forum, 7(36) (2012),
1751-1760.
Published
2020-09-08
How to Cite
Swamy, S. R., Darus, M., & Sailaja, Y. (2020). Properties On A New Comprehensive Family Of Holomorphic Functions Associated With Ruscheweyh Derivative and Generalized Multiplier Transformations. Journal of Progressive Research in Mathematics, 16(4), 3158-3166. Retrieved from https://scitecresearch.com/journals/index.php/jprm/article/view/1914
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