Coefficient-Related Studies and Fekete-Szegö Type Inequalities for New Classes of Bi-Starlike and Bi-Convex Functions
Abstract
:1. Introduction and Preliminaries
2. Set of Main Results
3. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Fekete, M.; Szegö, G. Eine bemerkung uber ungerade schlichte funktionen. J. London Math. Soc. 1933, 2, 85–89. [Google Scholar] [CrossRef]
- Abirami, C.; Magesh, N.; Yamini, J. Initial bounds for certain classes of bi-univalent functions defined by Horadam Polynomials. Abstr. Appl. Anal. 2020. [Google Scholar] [CrossRef] [Green Version]
- Al-Amoush, A.G. Coefficient estimates for a new subclasses of λ-pseudo biunivalent functions with respect to symmetrical points associated with the Horadam Polynomials. Turk. J. Math. 2019, 43, 2865–2875. [Google Scholar] [CrossRef]
- Güney, H.Ö.; Murugusundaramoorthy, G.; Sokół, J. Subclasses of bi-univalent functions related to shell-like curves connected with Fibonacci numbers. Acta Univ. Sapient. Math. 2018, 10, 70–84. [Google Scholar] [CrossRef] [Green Version]
- Srivastava, H.M.; Altınkaya, Ş.; Yalçin, S. Certain subclasses of bi-univalent functions associated with the Horadam polynomials. Iran. J. Sci. Technol. Trans. A Sci. 2019, 43, 1873–1879. [Google Scholar] [CrossRef]
- Srivastava, H.M.; Gaboury, S.; Ghanim, F. Coefficient estimates for some general subclasses of analytic and bi-univalent functions. Afr. Mat. 2017, 28, 693–706. [Google Scholar] [CrossRef]
- Srivastava, H.M.; Wanas, A.K. Applications of the Horadam polynomials involving λ-pseudo-starlike bi-univalent functions associated with a certain convolution operator. Filomat 2021, 35, 4645–4655. [Google Scholar] [CrossRef]
- Srivastava, H.M.; Wanas, A.K.; Güney, H.Ö. New families of bi-univalent functions associated with the Bazilevič functions and the λ-Pseudo-starlike functions. Iran. J. Sci. Technol. Trans. A Sci. 2021, 45, 1799–1804. [Google Scholar] [CrossRef]
- Srivastava, H.M.; Wanas, A.K.; Murugusundaramoorthy, G. Certain family of bi-univalent functions associated with Pascal distribution series based on Horadam polynomials. Surv. Math. Its Appl. 2021, 16, 193–205. [Google Scholar]
- Srivastava, H.M.; Wanas, A.K.; Srivastava, R. Applications of the q-Srivastava-Attiya operator involving a certain family of bi-univalent functions associated with the Horadam polynomials. Symmetry 2021, 13, 1230. [Google Scholar] [CrossRef]
- Wanas, A.K. Applications of (M,N)-Lucas polynomials for holomorphic and bi-univalent functions. Filomat 2020, 34, 3361–3368. [Google Scholar] [CrossRef]
- Srivastava, H.M.; Khan, B.; Khan, N.; Hussain, A.; Khan, N.; Tahir, M. Applications of certain basic (or q-) derivatives to subclasses of multivalent Janowski type q- starlike functions involving conic domains. J. Nonlinear Var. Anal. 2021, 5, 531–547. [Google Scholar]
- Wanas, A.K. Horadam polynomials for a new family of λ-pseudo bi-univalent functions associated with Sakaguchi type functions. Afr. Mat. 2021, 32, 879–889. [Google Scholar] [CrossRef]
- Srivastava, H.M.; Mishra, A.K.; Gochhayat, P. Certain subclasses of analytic and bi-univalent functions. Appl. Math. Lett. 2010, 23, 1188–1192. [Google Scholar] [CrossRef] [Green Version]
- Amourah, A. Fekete-Szegö inequalities for analytic and bi-univalent functions subordinate to (p,q)-Lucas Polynomials. arXiv 2020, arXiv:2004.00409. [Google Scholar]
- Amourah, A.; Frasin, B.A.; Abdeljaward, T. Fekete-Szegö inequality for analytic and bi-univalent functions subordinate to Gegenbauer polynomials. J. Funct. Spaces 2021. [Google Scholar] [CrossRef]
- Cataş, A. A note on subclasses of univalent functions defined by a generalized Sălăgean operator. Acta Univ. Apulensis 2006, 12, 73–78. [Google Scholar]
- Deniz, E. Sharp coefficient bounds for starlike functions associated with generalized telephone numbers. Bull. Malays. Math. Sci. Soc. 2021, 44, 1525–1542. [Google Scholar] [CrossRef]
- Yousef, F.; Frasin, B.A.; Al-Hawary, T. Fekete-Szego inequality for analytic and bi-univalent functions subordinate to Chebyshev polynomials. arXiv 2018, arXiv:1801.09531. [Google Scholar] [CrossRef]
- Magesh, N.; Yamini, J. Fekete-Szegö problem and second Hankel determinant for a class of bi-univalent functions. Tbilisi Math. J. 2018, 11, 141–157. [Google Scholar] [CrossRef] [Green Version]
- Páll-Szabó, A.O.; Oros, G.I. Coefficient Related Studies for New Classes of Bi-Univalent Functions. Mathematics 2020, 8, 1110. [Google Scholar] [CrossRef]
- Raina, R.K.; Sokol, J. Fekete-Szegö problem for some starlike functions related to shell-like curves. Math. Slovaca 2016, 66, 135–140. [Google Scholar] [CrossRef]
- Wanas, A.K.; Cotîrlǎ, L.-I. Initial coefficient estimates and Fekete–Szegö inequalities for new families of bi-univalent functions governed by (p-q)-Wanas operator. Symmetry 2021, 13, 2118. [Google Scholar] [CrossRef]
- Zaprawa, P. On the Fekete-Szegö problem for classes of bi-univalent functions. Bull. Belg. Math. Soc. Simon Stevin 2014, 21, 169–178. [Google Scholar] [CrossRef]
- Srivastava, H.M.; Arjika, S.; Kelil, A.S. Some homogeneous q- difference operators and the associated generalized Hahn polynomials. Appl. Set-Valued Anal. Optim. 2019, 1, 187–201. [Google Scholar]
- Miller, S.S.; Mocanu, P.T. Differential Subordinations: Theory and Applications; Series on Monographs and Textbooks in Pure and Applied Mathematics; Marcel Dekker Incorporated: New York, NY, USA; Basel, Switzerland, 2000; Volume 225. [Google Scholar]
- Duren, P.L. Univalent Functions; Grundlehren der Mathematischen Wissenschaften, Band 259; Springer: New York, NY, USA; Berlin/Heidelberg, Germany; Tokyo, Japan, 1983. [Google Scholar] [CrossRef]
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Cotîrlǎ, L.-I.; Wanas, A.K. Coefficient-Related Studies and Fekete-Szegö Type Inequalities for New Classes of Bi-Starlike and Bi-Convex Functions. Symmetry 2022, 14, 2263. https://doi.org/10.3390/sym14112263
Cotîrlǎ L-I, Wanas AK. Coefficient-Related Studies and Fekete-Szegö Type Inequalities for New Classes of Bi-Starlike and Bi-Convex Functions. Symmetry. 2022; 14(11):2263. https://doi.org/10.3390/sym14112263
Chicago/Turabian StyleCotîrlǎ, Luminiţa-Ioana, and Abbas Kareem Wanas. 2022. "Coefficient-Related Studies and Fekete-Szegö Type Inequalities for New Classes of Bi-Starlike and Bi-Convex Functions" Symmetry 14, no. 11: 2263. https://doi.org/10.3390/sym14112263
APA StyleCotîrlǎ, L.-I., & Wanas, A. K. (2022). Coefficient-Related Studies and Fekete-Szegö Type Inequalities for New Classes of Bi-Starlike and Bi-Convex Functions. Symmetry, 14(11), 2263. https://doi.org/10.3390/sym14112263