The Coefficient Estimates for A New Class of Analytic Functions with Negative Coefficients

Authors

  • Hanan Mohamed Almarwm Mathematics Department, Faculty of Science -Al-Khomus, Al-Margib University. Author
  • Aisha Ahmed Amer Mathematics Department, Faculty of Science -Al-Khomus, Al-Margib University. Author
  • Samah Khairi Ajaib Mathematics Department, Faculty of Science -Al-Khomus, Al-Margib University. Author

DOI:

https://doi.org/10.58916/jhas.v9i2.264

Keywords:

Analytic function, generalized derivative operator, Hadamard products, normalized power series, univalent functions.

Abstract

This paper introduces a new class in the open unit disc of analytic functions. It is mainly defined by the generalized derivative operator. A coefficient estimates is obtained, and other properties are derived. Additionally, Hadamard products (or convolution) of functions respective to the class are also included.

Downloads

Download data is not yet available.

References

Abufares ,F .and Amer .A , (2023) , Some Applications of Fractional Differential Operators in the Field of Geometric Function .Theory,Conference on basic sciences and their applications

Al-Oboudi, F.M. (2004) , On univalent functions defined by a generalized Sălăgean operator. International Journal of Mathematics and Mathematical Sciences,. p. 1429-1436.

Al-Shaqsi, K. and Darus . M , ( 2008 ), Differential subordination with generalized derivative operator. Int. J. Comp. Math. Sci,2 p. 75-78.

Al-Abbadi, M . and Darus . M, ( 2009) , Differential subordination for new generalised derivative operator. Acta Universitatis Apulensis. Mathematics-Informatics, 20. p. 265-280.

Alabbar. N, Darus. M & Amer.A. (2023), Coefficient Inequality and Coefficient Bounds for a New Subclass of Bazilevic Functions. Journal of Humanitarian and Applied Sciences, 8 -496-506.

Amer, A.A. and Darus. M , ( 2011), On some properties for new generalized derivative operator. Jordan Journal of Mathematics and Statistics (JJMS), 4 -(2): p. 91-101.

Amer.A , Darus , M and Alabbar .N .(2024) , Properties For Generalized Starlike and Convex Functions of Order , Fezzan University scientific Journal.

Annby. M. H and Mansour. Z. S, (2012) , q−Fractional Calculus Equations. Lecture Notes in Mathematics., Vol. 2056, Springer, Berlin.

Aouf. M. K. , Darwish. H. E and S˘al˘agean . G. S, (2001), , On a generalization of starlike functions with negative coefficients, Math., Tome 66 - no. 1, 3–10.

Catas, A. and Borsa .E , (2009). On a certain differential sandwich theorem associated with a new generalized derivative operator. General Mathematics, 17-p. 83-95

Frasin . B.A (2006), Family of analytic functions of complex order, Acta Math. Acad. Paedagogicae Ny , 22 -no. 2, 179–191.

Ismail. M.E, Merkes. M.E , and David. M.E, (1990), A generalization of starlike functions, Transit. Complex Variables, Theory Appl. 61 ,77–84.

Jackson. F. H, (1908), On q−functions and a certain difference operator, Trans. R. Soc. Edinb., 46-253–281.

Ruscheweyh, S. ( 1975 ). New criteria for univalent functions. Proceedings of the American Mathematical Society, 49 -(1): p. 109-115.

Salagean, G.S. (1981), Subclasses of univalent functions, Complex analysis-fifth Romanian-Finnish seminar, 1 , 362-372. Lecture Notes in Math, 1983.

SALEH .Z. M. , MOSTAFA. A. O. (2022), Class of analytic univalent functions with fixed finite negative coefficients defined by q-analogue difference operator, Jordan Journal of Mathematics and Statistics (JJMS), 15(4A), 2022, pp 955- 965

Shaqsi, K. and Darus . M , (2008) ,An operator defined by convolution involving the polylogarithms functions. Journal of Mathematics and Statistics, 4. (1): p. 46.

Shmella. E.K and Amer. A.A , (2023) , Estimation of the Bounds of Univalent Functional of Coefficients Apply the Subordination Method, The Academic Open Journal Of Applied And Human Sciences ,5,(2709-3344), issue (1) .

Silverman. H , (1975), Univalent functions with negative coefficients, Proc. Amer. Math. Soc. 51 ,no. 1, 109–116.

Published

2024-06-09

How to Cite

Hanan Mohamed Almarwm, Aisha Ahmed Amer, & Samah Khairi Ajaib. (2024). The Coefficient Estimates for A New Class of Analytic Functions with Negative Coefficients. Bani Waleed University Journal of Humanities and Applied Sciences, 9(2), 322-329. https://doi.org/10.58916/jhas.v9i2.264

Similar Articles

1-10 of 39

You may also start an advanced similarity search for this article.