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Integral transforms of certain subclasses of analytic functions. (English) Zbl 0982.44001
For the class ${\cal A}$ of normalized analytic functions in the unit disk a special integral transform ${\cal V}_\lambda$ is defined. If the functions $f$ belong to a subclass of ${\cal A}$, conditions are presented such that ${\cal V}_\lambda(f)$ is starlike and belongs to another subclass of ${\cal A}$. Some examples are given in order to show the improvement of earlier results.

MSC:
44A15Special transforms (Legendre, Hilbert, etc.)
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References:
[1] Andrews, G. E.; Askey, R.; Roy, R.: Special functions. (1999) · Zbl 0920.33001
[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) · Zbl 1097.30508
[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) · Zbl 0499.30001