Abstract
Recently, Mittag-Leffler function acts as beneficial role in studies of univalent functions. In this paper, motivated by some recent works, two new subclasses of univalent functions involving q−Mittag-Leffler function are introduced. Also, convolution conditions and coefficient estimates for these classes are investigated. The obtained results are presented in comparison with the results in the literature.
References
- [1] J. W. Alexander, “Functions which map the interior of the unit circle upon simple regions,” Ann. Math., 17, 12-22, 1915-1916.
- [2] T. M. Seoudy and M. K. Aouf, “Convolution properties for certain classes of analytic functions defined by q−derivative operator,” Abstract and Applied Analysis, Volume 2014, Article ID 846719, 7 pages.
- [3] D. Bansal and J. K. Prajabat, “Certain geometric properties of the Mittag-Leffler functions,” Complex Var. Elliptic Eq., 61, 338-350, 2016.
- [4] R. Gorenflo, A. A. Kilbas, F. Mainardi and S. V. Rogosin, “Mittag-Leffler functions, related topics and applications,” Springer, New-York, 2014.
- [5] A. W. Goodman, “Univalent functions,” Volume I and Volume II. Mariner Pub. Co. Inc. Tampa Florida, 1984.
- [6] F. H. Jackson, “On q−functions and a certain difference operator,” Trans. Royal Soc, Edinburgh, 46, 253-281, 1909.
- [7] F. H. Jackson, “q−difference equations,” Amer. J. Math., 32, 305-314, 1910.
- [8] F. H. Jackson,“On q−definite integrals,” Quart. J. Pure Appl. Math., 41, 193-203, 1910.
- [9] W. Janowski, “Some extremal problems for certain families of analytic functions I” Ann. Polon. Math,. 28, 297-326, 1973.
- [10] V. Kac and P. Cheung, “Quantum calculus,” Springer, 2002.
- [11] W. C. Ma and D. Minda, “A unified treatment of some special classes of univalent functions,” In: Proceedings of the Conference on Complex Analysis, Tianjin, 157–169, 1992.
- [12] G. M. Mittag-Leffler, “Sur la nouvelle fonction Eα(x),” C. R. Acad. Sci. Paris, 137, 554-558, 1903.
- [13] S.K. Sharma and R. Jain, “On some properties of generalized q−Mittag-Leffler function,” Mathematica Aeterna, 4, 613–619, 2014.
- [14] A. Wiman, “Über den fundamental satz in der teorie der functionen Eα(x) ,”Acta Math., 29, 191-201, 1905.
Abstract
Son zamanlarda, Mittag-Leffler fonksiyonu yalınkat fonksiyonlar ile ilgili çalışmalarda önemli rol oynamaktadır. Bu makalede, yapılan son çalışmaların ışığında q−Mittag-Leffler fonksiyonu ile tanımlı yalınkat fonksiyonların iki yeni alt sınıfı tanımlanmıştır. Bu sınıflar için konvolüsyon koşulları ve katsayı tahminleri araştırılmıştır. Elde edilen bulgular literatürde olan bulgularla karşılaştırılarak sunulmuştur.
Keywords
Analitik fonksiyonlar yıldızıl fonksiyonlar konveks fonksiyonlar konvolüsyon katsayı tahmini
References
- [1] J. W. Alexander, “Functions which map the interior of the unit circle upon simple regions,” Ann. Math., 17, 12-22, 1915-1916.
- [2] T. M. Seoudy and M. K. Aouf, “Convolution properties for certain classes of analytic functions defined by q−derivative operator,” Abstract and Applied Analysis, Volume 2014, Article ID 846719, 7 pages.
- [3] D. Bansal and J. K. Prajabat, “Certain geometric properties of the Mittag-Leffler functions,” Complex Var. Elliptic Eq., 61, 338-350, 2016.
- [4] R. Gorenflo, A. A. Kilbas, F. Mainardi and S. V. Rogosin, “Mittag-Leffler functions, related topics and applications,” Springer, New-York, 2014.
- [5] A. W. Goodman, “Univalent functions,” Volume I and Volume II. Mariner Pub. Co. Inc. Tampa Florida, 1984.
- [6] F. H. Jackson, “On q−functions and a certain difference operator,” Trans. Royal Soc, Edinburgh, 46, 253-281, 1909.
- [7] F. H. Jackson, “q−difference equations,” Amer. J. Math., 32, 305-314, 1910.
- [8] F. H. Jackson,“On q−definite integrals,” Quart. J. Pure Appl. Math., 41, 193-203, 1910.
- [9] W. Janowski, “Some extremal problems for certain families of analytic functions I” Ann. Polon. Math,. 28, 297-326, 1973.
- [10] V. Kac and P. Cheung, “Quantum calculus,” Springer, 2002.
- [11] W. C. Ma and D. Minda, “A unified treatment of some special classes of univalent functions,” In: Proceedings of the Conference on Complex Analysis, Tianjin, 157–169, 1992.
- [12] G. M. Mittag-Leffler, “Sur la nouvelle fonction Eα(x),” C. R. Acad. Sci. Paris, 137, 554-558, 1903.
- [13] S.K. Sharma and R. Jain, “On some properties of generalized q−Mittag-Leffler function,” Mathematica Aeterna, 4, 613–619, 2014.
- [14] A. Wiman, “Über den fundamental satz in der teorie der functionen Eα(x) ,”Acta Math., 29, 191-201, 1905.
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Makaleler |
| Authors | |
| Publication Date | May 27, 2021 |
| Published in Issue | Year 2021 Volume: 16 Issue: 1 |
