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2017 | 71 | 1 |
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Convolution conditions for bounded \(\alpha\)-starlike functions of complex order

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EN
Let \(A\) be the class of analytic functions in the unit disc \(U\) of the complex plane \(\mathbb{C}\) with the normalization \(f(0)=f^{^{\prime }}(0)-1=0\). We introduce a subclass \(S_{M}^{\ast }(\alpha ,b)\) of \(A\), which unifies the classes of bounded starlike and convex functions of complex order. Making use of Salagean operator, a more general class \(S_{M}^{\ast }(n,\alpha ,b)\) (\(n\geq 0\)) related to \(S_{M}^{\ast }(\alpha ,b)\) is also considered under the same conditions. Among other things, we find convolution conditions for a function \(f\in A\) to belong to the class \(S_{M}^{\ast }(\alpha ,b)\). Several properties of the class \(S_{M}^{\ast }(n,\alpha ,b)\) are investigated.
Rocznik
Tom
71
Numer
1
Opis fizyczny
Daty
wydano
2017
online
2017-06-30
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Bibliografia
  • Aouf, M. K., Darwish, H. E., Attiya, A. A., On a class of certain analytic functions of complex order, Indian J. Pure Appl. Math. 32 (10) (2001), 1443-1452.
  • El-Ashwah, R. M., Some convolution and inclusion properties for subclasses of bounded univalent functions of complex order, Thai J. Math. 12 (2) (2014), 373-384.
  • Goodman, A. W., Univalent Functions, Vol. I, II, Tampa, Florida, 1983.
  • Kulshrestha, P. K., Bounded Robertson functions, Rend. Mat. 6 (1) (1976), 137-150.
  • Kulshrestha, P. K., Distortion of spiral-like mapping, Proc. Royal Irish Acad. 73A (1973) 1-5.
  • Libera, R. J., Univalent \(\lambda\)-spiral functions, Canad. J. Mat. 19 (1967) 449-456.
  • Nasr, M. A., Aouf, M. K., On convex functions of complex order, Mansoura Sci. Bull. 9 (1982), 565-582.
  • Nasr, M. A., Aouf, M. K., Bounded convex functions of complex order, Mansoura Sci. Bull. 10 (1983), 513-526.
  • Nasr, M. A., Aouf, M. K., Bounded starlike functions of complex order, Proc. Indian Acad. Sci. (Math. Sci.) 92 (2) (1983) 97-102.
  • Nasr, M. A., Aouf, M. K., Starlike functions of complex order, J. Natur. Sci. Math. 25 (1985), 1-12.
  • Padmanabhan, K. S., Ganesan, M. S., Convolution conditions for certain class of analytic functions, Indian J. Pure Appl. Math. 15 (1984), 777-780.
  • Robertson, M. S., On the theory of univalent functions, Ann. of Math. 37 (1936), 374-408.
  • Salagean, G. S., Subclasses of univalent functions, in: Complex Analysis – Fifth Romanian-Finnish Seminar (C. A. Cazacu, N. Boboc, M. Jurchescu, I. Suciu, eds.) Springer, Berlin–Heidelberg, 1983, 362-372.
  • Silverman, H., Silvia, E. M., Telage, D., Convolution conditions for convexity and starlikeness and spiral-likeness, Math. Z. 162 (1978), 125-130.
  • Sizuk, P. I., Regular functions \(f(z)\) for which \(zf'(z)\) is \(\lambda\)-spirallike, Proc. Amer. Math. Soc. 49 (1975), 151-160.
  • Singh, R., Singh, V., On a class of bounded starlike functions, Indian J. Pure Appl. Math. 5 (8) (1974), 733-754.
  • Wiatrowski, P., The coefficient of a certain family of holomorphic functions, Zeszyty Nauk. Uniw. Łódz. Nauki Mat. Przyrod. Ser. II No. 39 Mat. (1971), 75-85.
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Bibliografia
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bwmeta1.element.ojs-doi-10_17951_a_2017_71_1_65
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