Previous |  Up |  Next

Article

Keywords:
analytic function; univalent function; starlike function; strongly starlike function; convex function; close-to-convex function; Wright function; Bessel function; subordination of functions
Summary:
In the present paper, we investigate certain geometric properties and inequalities for the Wright function and mention a few important consequences of our main results. A nonlinear differential equation involving the Wright function is also investigated.
References:
[1] Bansal, D., Prajapat, J. K.: Certain geometric properties of the Mittag-Leffler functions. Complex Var. Elliptic Equ. 61 (2016), 338-350. DOI 10.1080/17476933.2015.1079628 | MR 3454110 | Zbl 1336.33039
[2] Baricz, Á., Kupán, P. A., Szász, R.: The radius of starlikeness of normalized Bessel functions of the first kind. Proc. Am. Math. Soc. 142 (2014), 2019-2025. DOI 10.1090/S0002-9939-2014-11902-2 | MR 3182021 | Zbl 1291.30062
[3] Baricz, Á., Ponnusamy, S.: Starlikeness and convexity of generalized Bessel functions. Integral Transforms Spec. Funct. 21 (2010), 641-653. DOI 10.1080/10652460903516736 | MR 2743533 | Zbl 1205.30010
[4] Baricz, Á., Szász, R.: The radius of convexity of normalized Bessel functions of the first kind. Anal. Appl. Singap. 12 (2014), 485-509. DOI 10.1142/S0219530514500316 | MR 3252850 | Zbl 1302.33003
[5] Brickman, L., MacGregor, T. H., Wilken, D. R.: Convex hulls of some classical families of univalent functions. Trans. Am. Math. Soc. 156 (1971), 91-107. DOI 10.2307/1995600 | MR 0274734 | Zbl 0227.30013
[6] Branges, L. de: A proof of the Bieberbach conjecture. Acta Math. 154 (1985), 137-152. DOI 10.1007/BF02392821 | MR 0772434 | Zbl 0573.30014
[7] Duren, P. L.: Univalent Functions. Grundlehren der Mathematischen Wissenschaften 259. Springer, New York (1983). MR 0708494 | Zbl 0514.30001
[8] Fejér, L.: Untersuchungen über Potenzreihen mit mehrfach monotoner Koeffizientenfolge. Acta Litt. Sci. Szeged 8 (1937), 89-115. Zbl 0016.10803
[9] Goodman, A. W.: Univalent Functions. Vol. I. Mariner Publishing, Tampa (1983). MR 0704183 | Zbl 1041.30500
[10] Gorenflo, R., Luchko, Y., Mainardi, F.: Analytic properties and applications of the Wright functions. Fract. Cal. Appl. Anal. 2 (1999), 383-414. MR 1752379 | Zbl 1027.33006
[11] Hallenbeck, D. J., Ruscheweyh, S.: Subordination by convex functions. Proc. Am. Math. Soc. 52 (1975), 191-195. DOI 10.2307/2040127 | MR 0374403 | Zbl 0311.30010
[12] Kiryakova, V.: Generalized Fractional Calculus and Applications. Pitman Research Notes in Mathematics Series 301. Longman Scientific & Technical, Harlow; John Wiley & Sons, New York (1994). MR 1265940 | Zbl 0882.26003
[13] Mainardi, F.: The fundamental solutions for the fractional diffusion-wave equation. Appl. Math. Lett. 9 (1996), 23-28. DOI 10.1016/0893-9659(96)00089-4 | MR 1419811 | Zbl 0879.35036
[14] Miller, S. S., Mocanu, P. T.: Univalence of Gaussian and confluent hypergeometric functions. Proc. Am. Math. Soc. 110 (1990), 333-342. DOI 10.2307/2048075 | MR 1017006 | Zbl 0707.30012
[15] Miller, S. S., Mocanu, P. T.: Differential Subordinations. Theory and Applications. Pure and Applied Mathematics 225. A Series of Monographs and Textbooks. Marcel Dekker, New York (2000). MR 1760285 | Zbl 0954.34003
[16] Mondal, S. R., Swaminathan, A.: Geometric properties of generalized Bessel functions. Bull. Malays. Math. Sci. Soc. (2) 35 (2012), 179-194. MR 2865131 | Zbl 1232.30013
[17] Mustafa, N.: Geometric properties of normalized Wright functions. Math. Comput. Appl. 21 (2016), Paper No. 14, 10 pages. DOI 10.3390/mca21020014 | MR 3520354
[18] Ozaki, S.: On the theory of multivalent functions II. Sci. Rep. Tokyo Bunrika Daigaku. Sect. A 4 (1941), 45-87. MR 0048577 | Zbl 0063.06075
[19] Piejko, K., Sokół, J.: On the convolution and subordination of convex functions. Appl. Math. Lett. 25 (2012), 448-453. DOI 10.1016/j.aml.2011.09.034 | MR 2856004 | Zbl 1250.30016
[20] Ponnusamy, S.: The Hardy spaces of hypergeometric functions. Complex Variables, Theory Appl. 29 (1996), 83-96. DOI 10.1080/17476939608814876 | MR 1382005 | Zbl 0845.30036
[21] Ponnusamy, S.: Close-to-convexity properties of Gaussian hypergeometric functions. J. Comput. Appl. Math. 88 (1998), 327-337. DOI 10.1016/S0377-0427(97)00221-5 | MR 1613250 | Zbl 0901.30007
[22] Prajapat, J. K.: Certain geometric properties of normalized Bessel functions. Appl. Math. Lett. 24 (2011), 2133-2139. DOI 10.1016/j.aml.2011.06.014 | MR 2826152 | Zbl 1231.33004
[23] Prajapat, J. K.: Certain geometric properties of the Wright function. Integral Transforms Spec. Funct. 26 (2015), 203-212. DOI 10.1080/10652469.2014.983502 | MR 3293039 | Zbl 1306.30006
[24] Ruscheweyh, S., Singh, V.: On the order of starlikeness of hypergeometric functions. J. Math. Anal. Appl. 113 (1986), 1-11. DOI 10.1016/0022-247X(86)90329-X | MR 0826655 | Zbl 0598.30021
[25] Szász, R., Kupán, P. A.: About the univalence of the Bessel functions. Stud. Univ. Babeş-Bolyai Math. 54 (2009), 127-132. MR 2486953 | Zbl 1240.30078
[26] Tuneski, N.: On some simple sufficient conditions for univalence. Math. Bohem. 126 (2001), 229-236. MR 1826485 | Zbl 0986.30012
[27] Wilf, H. S.: Subordinating factor sequences for convex maps of the unit circle. Proc. Am. Math. Soc. 12 (1961), 689-693. DOI 10.2307/2034857 | MR 0125214 | Zbl 0100.07201
[28] Wright, E. M.: On the coefficients of power series having exponential singularities. J. London Math. Soc. 8 (1933), 71-80. DOI 10.1112/jlms/s1-8.1.71 | MR 1574787 | Zbl 0006.19704
[29] Yağmur, N.: Hardy space of Lommel functions. Bull. Korean Math. Soc. 52 (2015), 1035-1046. DOI 10.4134/BKMS.2015.52.3.1035 | MR 3353311 | Zbl 1318.30038
[30] Ya{ğ}mur, N., Orhan, H.: Starlikeness and convexity of generalized Struve functions. Abstr. Appl. Anal. 2013 (2013), Article ID 954513, 6 pages. DOI 10.1155/2013/954513 | MR 3035216 | Zbl 1272.30033
[31] Yağmur, N., Orhan, H.: Hardy space of generalized Struve functions. Complex Var. Elliptic Equ. 59 (2014), 929-936. DOI 10.1080/17476933.2013.799148 | MR 3195920 | Zbl 1290.30066
Partner of
EuDML logo