Certain geometric properties of the generalized dini function
Resumen
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.
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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
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
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
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
A. Baricz, E. Deniz and N. Yagmur, Close-to-convexity of normalized Dini functions, Mathematische Nachrichten. (2016). https://doi.org/10.1002/mana.201500009
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
P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Band 259, Springer-Verlag, New York, Berlin, Heidelberg and Tokyo, 1983.
L. Fejer, Untersuchungen uber Potenzreihen mit mehrfach monotoner Koeffizientenfolge, Acta Literarum Sci., 8(1936), 89-115. https://doi.org/10.2307/1989642
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
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
S. S. Miller and P. T. Mocanu, Differential Subordinations, Theory and Applications, New York-Basel, Marcel Dekker, 2000. https://doi.org/10.1201/9781482289817
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
P. T. Mocanu, Some starlike conditions for analytic functions, Rev Roumaine Math Pures Appl. 33(1988),117-124.
S. Ozaki, On the theory of multivalent functions, Sci. Rep. Tokyo Bunrika Daigaku, A(2)(1935), 167-188.
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
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
S. Ponnusamy, The Hardy space of hypergeometric functions, Complex Variables Theory Appl, 1996, 29(1), 83-96. https://doi.org/10.1080/17476939608814876
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
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
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