Certain subclasses of bi-univalent functions defined by $q$-analogue of Ruscheweyh differential operator
DOI:
https://doi.org/10.5269/bspm.77821Resumen
In this paper, we find a new subclasses of the function class $\sum$ of bi-univalent functions defined in the open unit disk, which are associated with the $q$-analogue of Ruscheweyh differential operator and satisfy some subordination conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients $|v_2|$ and $|v_3|$ for functions in the new subclasses introduced here.
Referencias
1. Aldweby, H. and Darus, M., Some subordination results on q-analogue of Ruscheweyh differential operator, Abstr. Appl. Anal., Volume 2014, Article Id: 958563, 6 Pages, (2014).
2. Brannan, D. A. and Clunie, J. and Kirwan, W. E., Coefficient estimates for a class of star-like functions, Can. J. Math., 22, 476–485, (1970).
3. Brannan, D. A. and Taha, T. S., On some classes of bi-univalent functions, Stud. Univ. Babes,-Bolyai, Math., 31(2), 70–77, (1986).
4. Deniz, E., Certain subclasess of bi-univalent functions satisfying subordinate conditions, Journal of Classical Analysis, 2(1), 49–60, (2013).
5. Jackson, F. H., XI. On q-Functions and a certain Difference Operator, Transactions of the Royal Society of Edinburgh, 46(2), 253–281, (1909).
6. Latha, T. J. and Indrani, S. C. M., Coefficient Estimates for Bi-univalent Ma-Minda Starlike and Convex Functions, Journal of Emerging Technologies and Innovative Research, 6(6), 68–74, (2019).
7. Kanas, S. and Raducanu, D., Some class of analytic functions related to conic domains, Math. Slovaca, 64(5), 1183–1196, (2014).
8. Lewin, M., On a coefficient problem for bi-univalent functions, Proc. Am. Math. Soc., 18, 63–68, (1967).
9. Ma, W. and Minda, D., A unified treatment of some special classes of univalent functions, Proceedings of the conference on complex analysis, held June 19-23, 1992 at the Nankai Institute of Mathematics, Tianjin, China, Cambridge, MA: International Press, Pages 157–169, (1994).
10. Ruscheweyh, S., New criteria for univalent functions, Proc. Am. Math. Soc., 49, 109–115, (1975).
11. Srivastava, H. M., Mishra, A. K. and Gochhayat, P., Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., 23(10), 1188–1192, (2010).
12. Hayami, T. and Owa, S., Coefficient bounds for bi-univalent functions, Panam. Math. J., 22(4), 15–26, (2012).
13. Xu. Q-H., Srivastava, H. M. and Li, Z., A certain subclass of analytic and close-to-convex functions, Appl. Math. Lett., 24(3), 396–401, (2011).
14. Li, X-F. and Wang, A-P., Two new subclasses of bi-univalent functions, Int. Math. Forum, 7, 1495–1504, (2012).
2. Brannan, D. A. and Clunie, J. and Kirwan, W. E., Coefficient estimates for a class of star-like functions, Can. J. Math., 22, 476–485, (1970).
3. Brannan, D. A. and Taha, T. S., On some classes of bi-univalent functions, Stud. Univ. Babes,-Bolyai, Math., 31(2), 70–77, (1986).
4. Deniz, E., Certain subclasess of bi-univalent functions satisfying subordinate conditions, Journal of Classical Analysis, 2(1), 49–60, (2013).
5. Jackson, F. H., XI. On q-Functions and a certain Difference Operator, Transactions of the Royal Society of Edinburgh, 46(2), 253–281, (1909).
6. Latha, T. J. and Indrani, S. C. M., Coefficient Estimates for Bi-univalent Ma-Minda Starlike and Convex Functions, Journal of Emerging Technologies and Innovative Research, 6(6), 68–74, (2019).
7. Kanas, S. and Raducanu, D., Some class of analytic functions related to conic domains, Math. Slovaca, 64(5), 1183–1196, (2014).
8. Lewin, M., On a coefficient problem for bi-univalent functions, Proc. Am. Math. Soc., 18, 63–68, (1967).
9. Ma, W. and Minda, D., A unified treatment of some special classes of univalent functions, Proceedings of the conference on complex analysis, held June 19-23, 1992 at the Nankai Institute of Mathematics, Tianjin, China, Cambridge, MA: International Press, Pages 157–169, (1994).
10. Ruscheweyh, S., New criteria for univalent functions, Proc. Am. Math. Soc., 49, 109–115, (1975).
11. Srivastava, H. M., Mishra, A. K. and Gochhayat, P., Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., 23(10), 1188–1192, (2010).
12. Hayami, T. and Owa, S., Coefficient bounds for bi-univalent functions, Panam. Math. J., 22(4), 15–26, (2012).
13. Xu. Q-H., Srivastava, H. M. and Li, Z., A certain subclass of analytic and close-to-convex functions, Appl. Math. Lett., 24(3), 396–401, (2011).
14. Li, X-F. and Wang, A-P., Two new subclasses of bi-univalent functions, Int. Math. Forum, 7, 1495–1504, (2012).
Descargas
Publicado
2025-08-24
Número
Sección
Research Articles
Licencia
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
Cómo citar
N. Ravikumar, M. Madhushree, & Siva Kota Reddy, P. (2025). Certain subclasses of bi-univalent functions defined by $q$-analogue of Ruscheweyh differential operator. Boletim Da Sociedade Paranaense De Matemática, 43, 1-8. https://doi.org/10.5269/bspm.77821
