Some Sufficient Conditions Involving Coefficient Inequalities in New Classes

Authors

  • Aisha Amer Mathematics Department, Faculty of Science -Al-Khomus, Al-Margib University Author
  • Nagat Alabbar Mathematics Department, Faculty of Education of Benghazi, University of Benghazi Author
  • Maslina Darus School of Mathematical Sciences, Faculty of Science and Technology Universiti Kebangsaan Malaysia Author

DOI:

https://doi.org/10.58987/p3zv1f51

Keywords:

Hadamard product, Univalent functions, Starlike functions, Convex functions, Linear operator

Abstract

In the present study, we introduce new classes of univalent functions denoted by Vl(m,λ)(a,b,c,α) and Vl(m,λ(a,b,c,α,θ) by a linear operator. These classes are related to the classes of starlike and convex functions. This research also discusses several interesting sufficient conditions involving coefficient inequalities for these classes. Additionally, several new results are shown after specializing the parameters employed in main results.

References

[1] W. Goodman, “Univalent functions,” Polygonal Publishing House, Washington, Vol. I and II, 1983.

[2] W. Kaplan, “Close-to-convex schlicht functions,” Michigan Mathematical Journal, Vol. 1(2), 169–185,1952. DOI: https://doi.org/10.1307/mmj/1028988895

[3] S. Salagean, “Subclasses of univalent functions,” Lecture notes in math. (Springer-Verlag), 1013, 362-372, 1983. DOI: https://doi.org/10.1007/BFb0066543

[4] A. Catas, “On a Certain Differential Sandwich Theorem Associated with a New Generalized Derivative Operator,” General Mathematics, Vol. 4, 83-95, 2009.

[5] S. Ruscheweyh, “New criteria for univalent functions,” Proc. Amer. Math. Soc. Vol. 49, 109-115, 1975. DOI: https://doi.org/10.1090/S0002-9939-1975-0367176-1

[6] A.A. Amer, M. Darus, N.M. Alabbar, “Properties for Generalized Starlike and Convex Functions of Order α,” Fezzan University Scientific Journal, Vol. 3(1), 423-429, 2024.

[7] N.M Alabbar, M. Darus. A.A. Amer, “Coefficient Inequality and Coefficient Bounds for a New Subclass of Bazilevic Functions,” Journal of Humanitarian and Applied Sciences, Vol. 8, 496-506, 2023. DOI: https://doi.org/10.65137/jhas.v8i16.467

[8] N.M Alabbar, A.A. Amer, “Properties of Generalized Derivative Operator to A Certain Subclass of Analytic Functions with Negative Coefficients,” Global Libyan Journal Vol. 2, 2017.

[9] N.M. Mustafa, M. Darus, “Some properties of a subclass of analytic function defined by a generalized Srivastava and Attiya operator,” Facta Universitatis (NIS), Vol. 27(3), 309-320, 2012.

[10] F. Al-Oboudi, “On univalent functions defined by a generalised Salagean Operator,” Int, J. Math. Math. Sci. Vol. 27, 1429-1436,2004. DOI: https://doi.org/10.1155/S0161171204108090

[11] A.A. Amer, M. Darus, N.M. Alabbar, “Necessary conditions for the generalized derivative operator in classes of univalent functions,” Academy journal for Basic and Applied Sciences, Vol. 6(2), 1-15, August 2024.

[12] E. Shmella, A.A. Amer, “Estimation of the bounds of univalent functional of coefficients apply the subordination method,” The Academic Open Journal of Applied And Human Sciences, Vol. 5(1), 2709-3344, 2023.

[13] E. Shmella, A.A. Amer, “Some properties of differential subordination for the subordination class with the generalized derivative operator,” Bani Waleed University Journal of Humanities and Applied Sciences, Vol. 2, 390-400, 2024.

[14] A.A. Amer, M. Darus, “On some properties for new generalized derivative operator,” Jordan Journal of Mathematics and Statistics, Vol. 4, 91-101, 2011.

[15] F.A. Abufares, A.A. Amer, “Certain applications of analytic functions associated in complex BB differential equations,” Journal of the Faculty of Education Tripoli, 19(1), 264-274, 2024.

[16] A.A. Amer, “Second Hankel determinant for new subclass defined by a linear operator,” Springer International Publishing Switzerland, Chapter 6, 2016. DOI: https://doi.org/10.1007/978-3-319-28443-9_6

[17] A.A. Amer. M. Darus, “Some Properties of the Class of Univalent Functions with Negative Coefficients” Applied Mathematics, Vol. 3, 1851-1856, 2012. DOI: https://doi.org/10.4236/am.2012.312251

[18] C. Carlson, B. Shaffer, “Starlike and prestarlike hypergeometric functions,” SIAM J. Math. Anal. Vol. 15(4), 737-745, 1984. DOI: https://doi.org/10.1137/0515057

[19] S. Owa, H. M. Srivastava, “Univalent and starlike generalized hypergeometric functions,” Can. J. Math, Vol. 39, 1057-1077, 1987. DOI: https://doi.org/10.4153/CJM-1987-054-3

[20] H.M. Srivastava, S. Owa, (Editors), “Current Topics in Analytic Function Theory,” World Scientific Publishing Company, Singapore, New Jersey, London and Hong Kong, 1992. DOI: https://doi.org/10.1142/1628

[21] T. Hayami, S. Owa, H.M. Srivastava, “Coefficient inequalities for certain classes of analytic and univalent functions,” J. Ineq. Pure Appl. Math. Vol. 8(4), 95, 1-10, 2007.

[22] S. Latha, O. Karthiyayini, “Certain class of analytic and univalent functions involving the Ruscheweyh derivative operator,” Int. Journal of Math. Analysis, Vol. 3(33), 1633–1644, 2009.

[23] H.M. Srivastava, S. Owa, S. Chatterjea, “A note on certain classes of starlike functions,” Rendiconti del Seminario Matematico della University di Padova, tome Vol. 77, 115-124, 1987.

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Published

2025-06-30

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How to Cite

Some Sufficient Conditions Involving Coefficient Inequalities in New Classes. (2025). Derna University Journal of Applied Sciences, 2(1), 87-99. https://doi.org/10.58987/p3zv1f51

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