Starlikeness and convexity of generalized Struve functions. (English) Zbl 1272.30033

Summary: We give sufficient conditions for the parameters of the normalized form of the generalized Struve functions to be convex and starlike in the open unit disk.


30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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[1] Baricz, A., Geometric properties of generalized Bessel functions, Publicationes Mathematicae Debrecen, 73, 1-2, 155-178 (2008) · Zbl 1156.33302
[2] Deniz, E.; Orhan, H.; Srivastava, H. M., Some sufficient conditions for univalence of certain families of integral operators involving generalized Bessel functions, Taiwanese Journal of Mathematics, 15, 2, 883-917 (2011) · Zbl 1242.30011
[3] Deniz, E., Convexity of integral operators involving generalized Bessel functions, Integral Transforms and Special Functions, 1, 1-16 (2012)
[4] Owa, S.; Srivastava, H. M., Univalent and starlike generalized hypergeometric functions, Canadian Journal of Mathematics, 39, 5, 1057-1077 (1987) · Zbl 0611.33007
[5] Selinger, V., Geometric properties of normalized Bessel functions, Pure Mathematics and Applications, 6, 2-3, 273-277 (1995) · Zbl 0867.30006
[6] Srivastava, H. M.; Yang, D.-G.; Xu, N.-E., Subordinations for multivalent analytic functions associated with the Dziok-Srivastava operator, Integral Transforms and Special Functions, 20, 7-8, 581-606 (2009) · Zbl 1170.30006
[7] Srivastava, H. M., Generalized hypergeometric functions and associated families of \(k\)-uniformly convex and \(k\)-starlike functions, General Mathematics, 15, 3, 201-226 (2007) · Zbl 1199.30107
[8] Srivastava, H. M.; Murugusundaramoorthy, G.; Sivasubramanian, S., Hypergeometric functions in the parabolic starlike and uniformly convex domains, Integral Transforms and Special Functions, 18, 7-8, 511-520 (2007) · Zbl 1198.30013
[9] Răducanu, D.; Srivastava, H. M., A new class of analytic functions defined by means of a convolution operator involving the Hurwitz-Lerch zeta function, Integral Transforms and Special Functions, 18, 11-12, 933-943 (2007) · Zbl 1130.30003
[10] Duren, P. L., Univalent Functions. Univalent Functions, Fundamental Principles of Mathematical Sciences, 259, xiv+382 (1983), New York, NY, USA: Springer, New York, NY, USA
[11] Alexander, J. W., Functions which map the interior of the unit circle upon simple regions, Annals of Mathematics, 17, 1, 12-22 (1915) · JFM 45.0672.02
[12] Kaplan, W., Close-to-convex schlicht functions, The Michigan Mathematical Journal, 1, 169-185 (1953) (1952) · Zbl 0048.31101
[13] Ozaki, S., On the theory of multivalent functions, Science Reports of the Tokyo Bunrika Daigaku, 2, 167-188 (1935) · JFM 61.0353.02
[14] Silverman, H., Univalent functions with negative coefficients, Proceedings of the American Mathematical Society, 51, 109-116 (1975) · Zbl 0311.30007
[15] Zhang, S.; Jin, J., Computation of Special Functions. Computation of Special Functions, A Wiley-Interscience Publication, xxvi+717 (1996), New York, NY, USA: John Wiley & Sons, New York, NY, USA
[16] Orhan, H.; Yağmur, N., Geometric properties of generalized Struve functions, The International Congress in Honour of Professor Hari M. Srivastava
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