Geometric properties of Wright function
Mathematica Bohemica, Tome 143 (2018) no. 1, pp. 99-111
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.21136/MB.2017.0077-16
Classification : 30C45, 33C10
Keywords: analytic function; univalent function; starlike function; strongly starlike function; convex function; close-to-convex function; Wright function; Bessel function; subordination of functions
@article{10_21136_MB_2017_0077_16,
     author = {Maharana, Sudhananda and Prajapat, Jugal K. and Bansal, Deepak},
     title = {Geometric properties of {Wright} function},
     journal = {Mathematica Bohemica},
     pages = {99--111},
     year = {2018},
     volume = {143},
     number = {1},
     doi = {10.21136/MB.2017.0077-16},
     mrnumber = {3778052},
     zbl = {06861594},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2017.0077-16/}
}
TY  - JOUR
AU  - Maharana, Sudhananda
AU  - Prajapat, Jugal K.
AU  - Bansal, Deepak
TI  - Geometric properties of Wright function
JO  - Mathematica Bohemica
PY  - 2018
SP  - 99
EP  - 111
VL  - 143
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2017.0077-16/
DO  - 10.21136/MB.2017.0077-16
LA  - en
ID  - 10_21136_MB_2017_0077_16
ER  - 
%0 Journal Article
%A Maharana, Sudhananda
%A Prajapat, Jugal K.
%A Bansal, Deepak
%T Geometric properties of Wright function
%J Mathematica Bohemica
%D 2018
%P 99-111
%V 143
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2017.0077-16/
%R 10.21136/MB.2017.0077-16
%G en
%F 10_21136_MB_2017_0077_16
Maharana, Sudhananda; Prajapat, Jugal K.; Bansal, Deepak. Geometric properties of Wright function. Mathematica Bohemica, Tome 143 (2018) no. 1, pp. 99-111. doi: 10.21136/MB.2017.0077-16

[1] Bansal, D., Prajapat, J. K.: Certain geometric properties of the Mittag-Leffler functions. Complex Var. Elliptic Equ. 61 (2016), 338-350. | DOI | MR | JFM

[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 | MR | JFM

[3] Baricz, Á., Ponnusamy, S.: Starlikeness and convexity of generalized Bessel functions. Integral Transforms Spec. Funct. 21 (2010), 641-653. | DOI | MR | JFM

[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 | MR | JFM

[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 | MR | JFM

[6] Branges, L. de: A proof of the Bieberbach conjecture. Acta Math. 154 (1985), 137-152. | DOI | MR | JFM

[7] Duren, P. L.: Univalent Functions. Grundlehren der Mathematischen Wissenschaften 259. Springer, New York (1983). | MR | JFM

[8] Fejér, L.: Untersuchungen über Potenzreihen mit mehrfach monotoner Koeffizientenfolge. Acta Litt. Sci. Szeged 8 (1937), 89-115. | JFM

[9] Goodman, A. W.: Univalent Functions. Vol. I. Mariner Publishing, Tampa (1983). | MR | JFM

[10] Gorenflo, R., Luchko, Y., Mainardi, F.: Analytic properties and applications of the Wright functions. Fract. Cal. Appl. Anal. 2 (1999), 383-414. | MR | JFM

[11] Hallenbeck, D. J., Ruscheweyh, S.: Subordination by convex functions. Proc. Am. Math. Soc. 52 (1975), 191-195. | DOI | MR | JFM

[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 | JFM

[13] Mainardi, F.: The fundamental solutions for the fractional diffusion-wave equation. Appl. Math. Lett. 9 (1996), 23-28. | DOI | MR | JFM

[14] Miller, S. S., Mocanu, P. T.: Univalence of Gaussian and confluent hypergeometric functions. Proc. Am. Math. Soc. 110 (1990), 333-342. | DOI | MR | JFM

[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 | JFM

[16] Mondal, S. R., Swaminathan, A.: Geometric properties of generalized Bessel functions. Bull. Malays. Math. Sci. Soc. (2) 35 (2012), 179-194. | MR | JFM

[17] Mustafa, N.: Geometric properties of normalized Wright functions. Math. Comput. Appl. 21 (2016), Paper No. 14, 10 pages. | DOI | MR

[18] Ozaki, S.: On the theory of multivalent functions II. Sci. Rep. Tokyo Bunrika Daigaku. Sect. A 4 (1941), 45-87. | MR | JFM

[19] Piejko, K., Sokół, J.: On the convolution and subordination of convex functions. Appl. Math. Lett. 25 (2012), 448-453. | DOI | MR | JFM

[20] Ponnusamy, S.: The Hardy spaces of hypergeometric functions. Complex Variables, Theory Appl. 29 (1996), 83-96. | DOI | MR | JFM

[21] Ponnusamy, S.: Close-to-convexity properties of Gaussian hypergeometric functions. J. Comput. Appl. Math. 88 (1998), 327-337. | DOI | MR | JFM

[22] Prajapat, J. K.: Certain geometric properties of normalized Bessel functions. Appl. Math. Lett. 24 (2011), 2133-2139. | DOI | MR | JFM

[23] Prajapat, J. K.: Certain geometric properties of the Wright function. Integral Transforms Spec. Funct. 26 (2015), 203-212. | DOI | MR | JFM

[24] Ruscheweyh, S., Singh, V.: On the order of starlikeness of hypergeometric functions. J. Math. Anal. Appl. 113 (1986), 1-11. | DOI | MR | JFM

[25] Szász, R., Kupán, P. A.: About the univalence of the Bessel functions. Stud. Univ. Babeş-Bolyai Math. 54 (2009), 127-132. | MR | JFM

[26] Tuneski, N.: On some simple sufficient conditions for univalence. Math. Bohem. 126 (2001), 229-236. | MR | JFM

[27] Wilf, H. S.: Subordinating factor sequences for convex maps of the unit circle. Proc. Am. Math. Soc. 12 (1961), 689-693. | DOI | MR | JFM

[28] Wright, E. M.: On the coefficients of power series having exponential singularities. J. London Math. Soc. 8 (1933), 71-80. | DOI | MR | JFM

[29] Yağmur, N.: Hardy space of Lommel functions. Bull. Korean Math. Soc. 52 (2015), 1035-1046. | DOI | MR | JFM

[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 | MR | JFM

[31] Yağmur, N., Orhan, H.: Hardy space of generalized Struve functions. Complex Var. Elliptic Equ. 59 (2014), 929-936. | DOI | MR | JFM

Cité par Sources :