Certain geometric properties of the generalized dini function
DOI:
https://doi.org/10.5269/bspm.51198Abstract
In the present investigation we first introduce modified Dini function and then find sufficient conditions so that the modified Dini function have certain geometric properties like close-to-convexity, starlikeness and strongly starlikeness in the open unit disk. Some subordination sequences are also established.
References
1. D. Bansal and J. K. Prajapat, Certain geometric properties of the Mittag-Leffler functions, Complex Var. Elliptic Eq. 61(3) (2016), 338-350. https://doi.org/10.1080/17476933.2015.1079628
2. A. Baricz, P. A. Kupan and R. Szasz, The radius of starlikeness of normalized Bessel function of first kind, Proc. Amer. Math. Soc. 142(6) (2014), 2019-2025. https://doi.org/10.1090/S0002-9939-2014-11902-2
3. A. Baricz and S. Poonusamy, Starlikeness and convexity of generalized Bessel functions, Integral Transform Spec. Funct., 21(9) (2010), 641-653. https://doi.org/10.1080/10652460903516736
4. A. Baricz, S. Ponnusamy and S. Singh, Modified Dini functions: Monotonicity patterns and Functinal inequalities, Acta Mathematica Hungarica, 149(2016), 120-142. https://doi.org/10.1007/s10474-016-0599-9
5. A. Baricz, E. Deniz and N. Yagmur, Close-to-convexity of normalized Dini functions, Mathematische Nachrichten. (2016). https://doi.org/10.1002/mana.201500009
6. A. Baricz, T. K. Pogany and R. Szasz , Monotonicity properties of some Dini functions, Proceedings of the 9th IEEE International Symposium on Applied Computational Intelligence and Informatics, May 15-17, Timi¸soara, Romania, (2014) 323-326. https://doi.org/10.1109/SACI.2014.6840085
7. P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Band 259, Springer-Verlag, New York, Berlin, Heidelberg and Tokyo, 1983.
8. L. Fejer, Untersuchungen uber Potenzreihen mit mehrfach monotoner Koeffizientenfolge, Acta Literarum Sci., 8(1936), 89-115. https://doi.org/10.2307/1989642
9. D. J. Halenbeck and S. Ruscheweyh, Subordinations by convex functions, Proc. Amer. Math. Soc. 52 (1975), 191-195. https://doi.org/10.1090/S0002-9939-1975-0374403-3
10. S. S. Miller and P. T. Mocanu, Differential subordinates and inequities in the complex plane, J. Differ. Equations, 67 (1987), 199-211. https://doi.org/10.1016/0022-0396(87)90146-X
11. S. S. Miller and P. T. Mocanu, Differential Subordinations, Theory and Applications, New York-Basel, Marcel Dekker, 2000. https://doi.org/10.1201/9781482289817
12. S. S. Miller and P. T. Mocanu, Univalence of Gaussian and confluent hypergeometric functions, Proc. Amer. Math. Soc. 110(2) (1990), 333-342. https://doi.org/10.1090/S0002-9939-1990-1017006-8
13. P. T. Mocanu, Some starlike conditions for analytic functions, Rev Roumaine Math Pures Appl. 33(1988),117-124.
14. S. Ozaki, On the theory of multivalent functions, Sci. Rep. Tokyo Bunrika Daigaku, A(2)(1935), 167-188.
15. J. K. Prajapat, Certain geometric properties of the Wright functions, Integral Transform. Spec. Funct. 26(3) (2015), 203-212. https://doi.org/10.1080/10652469.2014.983502
16. S. Ponnusamy, Close-to-convexity properties of Gaussian hypergeometric functions, J. Comput. Appl. Maths, 1997, 88, 327-337. https://doi.org/10.1016/S0377-0427(97)00221-5
17. S. Ponnusamy, The Hardy space of hypergeometric functions, Complex Variables Theory Appl, 1996, 29(1), 83-96. https://doi.org/10.1080/17476939608814876
18. V. Singh and St. Ruscheweyh, On the order of starlikeness of hypergeometric functions, J. Math. Anal. Appl, 1986, 113, 1-11. https://doi.org/10.1016/0022-247X(86)90329-X
19. H. S., Wilf, Subordinating factor sequences for convex maps of the unit circle, Proc. Amer. Math. Soc., 12(1961), 689-693. https://doi.org/10.1090/S0002-9939-1961-0125214-5
2. A. Baricz, P. A. Kupan and R. Szasz, The radius of starlikeness of normalized Bessel function of first kind, Proc. Amer. Math. Soc. 142(6) (2014), 2019-2025. https://doi.org/10.1090/S0002-9939-2014-11902-2
3. A. Baricz and S. Poonusamy, Starlikeness and convexity of generalized Bessel functions, Integral Transform Spec. Funct., 21(9) (2010), 641-653. https://doi.org/10.1080/10652460903516736
4. A. Baricz, S. Ponnusamy and S. Singh, Modified Dini functions: Monotonicity patterns and Functinal inequalities, Acta Mathematica Hungarica, 149(2016), 120-142. https://doi.org/10.1007/s10474-016-0599-9
5. A. Baricz, E. Deniz and N. Yagmur, Close-to-convexity of normalized Dini functions, Mathematische Nachrichten. (2016). https://doi.org/10.1002/mana.201500009
6. A. Baricz, T. K. Pogany and R. Szasz , Monotonicity properties of some Dini functions, Proceedings of the 9th IEEE International Symposium on Applied Computational Intelligence and Informatics, May 15-17, Timi¸soara, Romania, (2014) 323-326. https://doi.org/10.1109/SACI.2014.6840085
7. P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Band 259, Springer-Verlag, New York, Berlin, Heidelberg and Tokyo, 1983.
8. L. Fejer, Untersuchungen uber Potenzreihen mit mehrfach monotoner Koeffizientenfolge, Acta Literarum Sci., 8(1936), 89-115. https://doi.org/10.2307/1989642
9. D. J. Halenbeck and S. Ruscheweyh, Subordinations by convex functions, Proc. Amer. Math. Soc. 52 (1975), 191-195. https://doi.org/10.1090/S0002-9939-1975-0374403-3
10. S. S. Miller and P. T. Mocanu, Differential subordinates and inequities in the complex plane, J. Differ. Equations, 67 (1987), 199-211. https://doi.org/10.1016/0022-0396(87)90146-X
11. S. S. Miller and P. T. Mocanu, Differential Subordinations, Theory and Applications, New York-Basel, Marcel Dekker, 2000. https://doi.org/10.1201/9781482289817
12. S. S. Miller and P. T. Mocanu, Univalence of Gaussian and confluent hypergeometric functions, Proc. Amer. Math. Soc. 110(2) (1990), 333-342. https://doi.org/10.1090/S0002-9939-1990-1017006-8
13. P. T. Mocanu, Some starlike conditions for analytic functions, Rev Roumaine Math Pures Appl. 33(1988),117-124.
14. S. Ozaki, On the theory of multivalent functions, Sci. Rep. Tokyo Bunrika Daigaku, A(2)(1935), 167-188.
15. J. K. Prajapat, Certain geometric properties of the Wright functions, Integral Transform. Spec. Funct. 26(3) (2015), 203-212. https://doi.org/10.1080/10652469.2014.983502
16. S. Ponnusamy, Close-to-convexity properties of Gaussian hypergeometric functions, J. Comput. Appl. Maths, 1997, 88, 327-337. https://doi.org/10.1016/S0377-0427(97)00221-5
17. S. Ponnusamy, The Hardy space of hypergeometric functions, Complex Variables Theory Appl, 1996, 29(1), 83-96. https://doi.org/10.1080/17476939608814876
18. V. Singh and St. Ruscheweyh, On the order of starlikeness of hypergeometric functions, J. Math. Anal. Appl, 1986, 113, 1-11. https://doi.org/10.1016/0022-247X(86)90329-X
19. H. S., Wilf, Subordinating factor sequences for convex maps of the unit circle, Proc. Amer. Math. Soc., 12(1961), 689-693. https://doi.org/10.1090/S0002-9939-1961-0125214-5
Downloads
Published
2022-12-23
Issue
Section
Research Articles
License
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).
