Integral transforms of certain subclasses of analytic functions. (English) Zbl 0982.44001

For the class \({\mathcal A}\) of normalized analytic functions in the unit disk a special integral transform \({\mathcal V}_\lambda\) is defined. If the functions \(f\) belong to a subclass of \({\mathcal A}\), conditions are presented such that \({\mathcal V}_\lambda(f)\) is starlike and belongs to another subclass of \({\mathcal A}\). Some examples are given in order to show the improvement of earlier results.


44A15 Special integral transforms (Legendre, Hilbert, etc.)
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[1] Andrews, G.E.; Askey, R.; Roy, R., Special functions, (1999), Cambridge Univ. Press Cambridge
[2] Carlson, B.C.; Shaffer, D.B., Starlike and prestarlike hypergeometric functions, SIAM J. math. anal., 15, 737-745, (1984) · Zbl 0567.30009
[3] Chichra, P.N., New subclasses of the class of close-to-convex functions, Proc. amer. math. soc., 62, 37-43, (1977) · Zbl 0355.30013
[4] Fourier, R.; Ruscheweyh, St., On two extremal problems related to univalent functions, Rocky mountain J. math., 24, 529-538, (1994) · Zbl 0818.30013
[5] Hallenbeck, D.J.; Ruscheweyh, St., Subordination by convex functions, Proc. amer. math. soc., 52, 191-195, (1975) · Zbl 0311.30010
[6] Kim, Y.C.; Lecko, A., Univalence of certain integral operators and differential subordination, Mathematica (cluj), 1, (2001)
[7] Komatu, Y., On analytic prolongation of a family of operators, Mathematica (cluj), 32, 141-145, (1990) · Zbl 0753.30005
[8] Owa, S.; Nunokawa, M., Application of a subordination theorem, J. math. anal. appl., 188, 219-226, (1994) · Zbl 0817.30009
[9] Ponnusamy, S., Differential subordination and starlike functions, Complex variables, 19, 185-194, (1992) · Zbl 0724.30020
[10] Ponnusamy, S.; Rønning, F., Duality for Hadamard products applied to certain integral transforms, Complex variables, 32, 263-287, (1997) · Zbl 0878.30007
[11] Ponnusamy, S.; Rønning, F., Geometric properties for convolutions of hypergeometric functions and functions with the derivative in a halfplane, Integral transforms special funct., 8, 121-138, (1999) · Zbl 0938.30006
[12] Ponnusamy, S.; Rønning, F., Integral transforms of functions with the derivative in a halfplane, Israel J. math., 114, 177-188, (1999) · Zbl 0943.30010
[13] Ruscheweyh, St., Convolutions in geometric function theory, (1982), Les Presses de l’Université de Montréal Montréal · Zbl 0575.30008
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