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Title: Geometric properties of Wright function (English)
Author: Maharana, Sudhananda
Author: Prajapat, Jugal K.
Author: Bansal, Deepak
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 143
Issue: 1
Year: 2018
Pages: 99-111
Summary lang: English
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Category: math
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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. (English)
Keyword: analytic function
Keyword: univalent function
Keyword: starlike function
Keyword: strongly starlike function
Keyword: convex function
Keyword: close-to-convex function
Keyword: Wright function
Keyword: Bessel function
Keyword: subordination of functions
MSC: 30C45
MSC: 33C10
idZBL: Zbl 06861594
idMR: MR3778052
DOI: 10.21136/MB.2017.0077-16
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Date available: 2018-03-19T10:35:51Z
Last updated: 2020-07-01
Stable URL: http://hdl.handle.net/10338.dmlcz/147144
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Reference: [1] Bansal, D., Prajapat, J. K.: Certain geometric properties of the Mittag-Leffler functions.Complex Var. Elliptic Equ. 61 (2016), 338-350. Zbl 1336.33039, MR 3454110, 10.1080/17476933.2015.1079628
Reference: [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. Zbl 1291.30062, MR 3182021, 10.1090/S0002-9939-2014-11902-2
Reference: [3] Baricz, Á., Ponnusamy, S.: Starlikeness and convexity of generalized Bessel functions.Integral Transforms Spec. Funct. 21 (2010), 641-653. Zbl 1205.30010, MR 2743533, 10.1080/10652460903516736
Reference: [4] Baricz, Á., Szász, R.: The radius of convexity of normalized Bessel functions of the first kind.Anal. Appl. Singap. 12 (2014), 485-509. Zbl 1302.33003, MR 3252850, 10.1142/S0219530514500316
Reference: [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. Zbl 0227.30013, MR 0274734, 10.2307/1995600
Reference: [6] Branges, L. de: A proof of the Bieberbach conjecture.Acta Math. 154 (1985), 137-152. Zbl 0573.30014, MR 0772434, 10.1007/BF02392821
Reference: [7] Duren, P. L.: Univalent Functions.Grundlehren der Mathematischen Wissenschaften 259. Springer, New York (1983). Zbl 0514.30001, MR 0708494
Reference: [8] Fejér, L.: Untersuchungen über Potenzreihen mit mehrfach monotoner Koeffizientenfolge.Acta Litt. Sci. Szeged 8 (1937), 89-115. Zbl 0016.10803
Reference: [9] Goodman, A. W.: Univalent Functions. Vol. I.Mariner Publishing, Tampa (1983). Zbl 1041.30500, MR 0704183
Reference: [10] Gorenflo, R., Luchko, Y., Mainardi, F.: Analytic properties and applications of the Wright functions.Fract. Cal. Appl. Anal. 2 (1999), 383-414. Zbl 1027.33006, MR 1752379
Reference: [11] Hallenbeck, D. J., Ruscheweyh, S.: Subordination by convex functions.Proc. Am. Math. Soc. 52 (1975), 191-195. Zbl 0311.30010, MR 0374403, 10.2307/2040127
Reference: [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). Zbl 0882.26003, MR 1265940
Reference: [13] Mainardi, F.: The fundamental solutions for the fractional diffusion-wave equation.Appl. Math. Lett. 9 (1996), 23-28. Zbl 0879.35036, MR 1419811, 10.1016/0893-9659(96)00089-4
Reference: [14] Miller, S. S., Mocanu, P. T.: Univalence of Gaussian and confluent hypergeometric functions.Proc. Am. Math. Soc. 110 (1990), 333-342. Zbl 0707.30012, MR 1017006, 10.2307/2048075
Reference: [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). Zbl 0954.34003, MR 1760285
Reference: [16] Mondal, S. R., Swaminathan, A.: Geometric properties of generalized Bessel functions.Bull. Malays. Math. Sci. Soc. (2) 35 (2012), 179-194. Zbl 1232.30013, MR 2865131
Reference: [17] Mustafa, N.: Geometric properties of normalized Wright functions.Math. Comput. Appl. 21 (2016), Paper No. 14, 10 pages. MR 3520354, 10.3390/mca21020014
Reference: [18] Ozaki, S.: On the theory of multivalent functions II.Sci. Rep. Tokyo Bunrika Daigaku. Sect. A 4 (1941), 45-87. Zbl 0063.06075, MR 0048577
Reference: [19] Piejko, K., Sokół, J.: On the convolution and subordination of convex functions.Appl. Math. Lett. 25 (2012), 448-453. Zbl 1250.30016, MR 2856004, 10.1016/j.aml.2011.09.034
Reference: [20] Ponnusamy, S.: The Hardy spaces of hypergeometric functions.Complex Variables, Theory Appl. 29 (1996), 83-96. Zbl 0845.30036, MR 1382005, 10.1080/17476939608814876
Reference: [21] Ponnusamy, S.: Close-to-convexity properties of Gaussian hypergeometric functions.J. Comput. Appl. Math. 88 (1998), 327-337. Zbl 0901.30007, MR 1613250, 10.1016/S0377-0427(97)00221-5
Reference: [22] Prajapat, J. K.: Certain geometric properties of normalized Bessel functions.Appl. Math. Lett. 24 (2011), 2133-2139. Zbl 1231.33004, MR 2826152, 10.1016/j.aml.2011.06.014
Reference: [23] Prajapat, J. K.: Certain geometric properties of the Wright function.Integral Transforms Spec. Funct. 26 (2015), 203-212. Zbl 1306.30006, MR 3293039, 10.1080/10652469.2014.983502
Reference: [24] Ruscheweyh, S., Singh, V.: On the order of starlikeness of hypergeometric functions.J. Math. Anal. Appl. 113 (1986), 1-11. Zbl 0598.30021, MR 0826655, 10.1016/0022-247X(86)90329-X
Reference: [25] Szász, R., Kupán, P. A.: About the univalence of the Bessel functions.Stud. Univ. Babeş-Bolyai Math. 54 (2009), 127-132. Zbl 1240.30078, MR 2486953
Reference: [26] Tuneski, N.: On some simple sufficient conditions for univalence.Math. Bohem. 126 (2001), 229-236. Zbl 0986.30012, MR 1826485
Reference: [27] Wilf, H. S.: Subordinating factor sequences for convex maps of the unit circle.Proc. Am. Math. Soc. 12 (1961), 689-693. Zbl 0100.07201, MR 0125214, 10.2307/2034857
Reference: [28] Wright, E. M.: On the coefficients of power series having exponential singularities.J. London Math. Soc. 8 (1933), 71-80. Zbl 0006.19704, MR 1574787, 10.1112/jlms/s1-8.1.71
Reference: [29] Yağmur, N.: Hardy space of Lommel functions.Bull. Korean Math. Soc. 52 (2015), 1035-1046. Zbl 1318.30038, MR 3353311, 10.4134/BKMS.2015.52.3.1035
Reference: [30] Ya{ğ}mur, N., Orhan, H.: Starlikeness and convexity of generalized Struve functions.Abstr. Appl. Anal. 2013 (2013), Article ID 954513, 6 pages. Zbl 1272.30033, MR 3035216, 10.1155/2013/954513
Reference: [31] Yağmur, N., Orhan, H.: Hardy space of generalized Struve functions.Complex Var. Elliptic Equ. 59 (2014), 929-936. Zbl 1290.30066, MR 3195920, 10.1080/17476933.2013.799148
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