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2012 | 66 | 1 |
Tytuł artykułu

On certain general integral operators of analytic functions

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EN
Abstrakty
EN
In this paper, we obtain new sufficient conditions for the operators \(F_{\alpha_1,\alpha_2,...,\alpha_n,\beta}(z)\) and \(G_{\alpha_1,\alpha_2,...,\alpha_n,\beta}(z)\) to be univalent in the open unit disc \(\mathcal{U}\), where the functions \(f_1, f_2,..., f_n\) belong to the classes \(S^*(a, b)\) and \(\mathcal{K}(a, b)\). The order of convexity for the operators \(F_{\alpha_1,\alpha_2,...,\alpha_n,\beta}(z)\) and \(G_{\alpha_1,\alpha_2,...,\alpha_n,\beta}(z)\) is also determined. Furthermore, and for \(\beta= 1\), we obtain sufficient conditions for the operators \(F_n(z)\) and \(G_n(z)\) to be in the class \(\mathcal{K}(a, b)\). Several corollaries and consequences of the main results are also considered.
Rocznik
Tom
66
Numer
1
Opis fizyczny
Daty
wydano
2012
online
2016-07-24
Twórcy
autor
Bibliografia
  • Ahlfors, L. V., Sufficient conditions for quasiconformal extension, Discontinuous groups and Riemann surfaces (Proc. Conf., Univ. Maryland, College Park, Md., 1973), pp. 23-29. Ann. of Math. Studies, No. 79, Princeton Univ. Press, Princeton, N.J., 1974.
  • Becker, J., Lownersche Differentialgleichung und quasikonform fortsetzbare schlichte Funktionen, J. Reine Angew. Math. 255 (1972), 23-43.
  • Becker, J., Lownersche Differentialgleichung und Schlichtheitskriterien, Math. Ann. 202 (1973), 321-335.
  • Breaz, D., Univalence properties for a general integral operator, Bull. Korean Math. Soc. 46 (2009), no. 3, 439-446.
  • Breaz, D., Breaz, N., Two integral operators, Studia Universitatis Babes-Bolyai Math., 47 (2002), no. 3, 13-19.
  • Breaz, D., Breaz, N., Univalence conditions for certain integral operators, Studia Universitatis Babes-Bolyai, Mathematica, 47 (2002), no. 2, 9-15.
  • Breaz, D., Owa, S., Some extensions of univalent conditions for certain integral operators, Math. Inequal. Appl., 10 (2007), no. 2, 321-325.
  • Bulut, S., Univalence preserving integral operators defined by generalized Al- Oboudi differential operators, An. S¸tiint¸. Univ. ”Ovidius” Constant¸a Ser. Mat. 17 (2009), no. 1, 37-50.
  • Eenigenburg, P., Miller, S. S., Mocanu, P. T. and Reade, M. O., On a Briot–Bouquet differential subordination, General inequalities, 3 (Oberwolfach, 1981), 339-348, Internat. Schriftenreihe Numer. Math., 64, Birkhauser, Basel, 1983.
  • Frasin, B. A., General integral operator defined by Hadamard product, Mat. Vesnik 62 (2010), no. 2, 127-136.
  • Frasin. B. A., Aouf, M. K., Univalence conditions for a new general integral operator, Hacet. J. Math. Stat. 39 (2010), no. 4, 567-575.
  • Jabkubowski, Z. J., On the coefficients of starlike functions of some classes, Ann. Polon. Math. 26 (1972), 305-313.
  • Pascu, N., An improvement of Becker’s univalence criterion, Proceedings of the Commemorative Session: Simion Stoılow (Brasov, 1987), 43-48, Univ. Brasov, Brasov, 1987.
  • Pescar, V., A new generalization of Ahlfor’s and Becker’s criterion of univalence, Bull. Malaysian Math. Soc. (2) 19 (1996), no. 2, 53-54.
  • Seenivasagan, N., Sufficient conditions for univalence, Applied Math. E-Notes, 8 (2008), 30-35.
  • Seenivasagan, N., Breaz, D., Certain sufficient conditions for univalence, Gen. Math. 15 (2007), no. 4, 7-15.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.ojs-doi-10_17951_a_2012_66_1_13-23
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