Univalence Conditions for a New General Integral Operator  ABSTRACT  |  FULL TEXT

Yıl 2010, Cilt: 39 Sayı: 4, 567 - 575, 01.04.2010

B.a. Frasin  m.k. Aouf

Öz

Using the Hadamard product, we define a new general integral operator.
The aim of this paper is to obtain new sufficient conditions for the
univalence of this general integral operator. Several corollaries and
consequences of the main results are also considered.

Anahtar Kelimeler

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Univalence Conditions for a New General Integral Operator  ABSTRACT  |  FULL TEXT

Öz

Kaynakça

• Al-Oboudi, F. M. On univalent functions defined by a generalized Salagean operator, Int. J. Math. Math. Sci. 27, 1429–1436, 2004.
• Breaz, D. and Breaz, N. An integral univalent operator, Acta Math. Univ. Comenianae LXXVI(2), 137–142, 2007. [3] Breaz, D. and Breaz, N. Univalence of an integral operator, Mathematica (Cluj) 47 (70), 35–38, 2005.
• Breaz, D., Breaz, N. and Srivastava, H. M. An extension of the univalent condition for a family of integral operators, Appl. Math. Lett. 22 (1), 41–44, 2009.
• Bulut, S. Univalence condition for a new generalization of the family of integral operators, Acta Univ. Apu. 18, 71–78, 2009.
• Dziok, J. and Srivastava, H. M. Classes of analytic functions associated with the generalized hypergeometric function,Appl. Math. Comput. 103, 1–13, 1999.
• Frasin, B. A. General integral operator defined by Hadamard product, Matematicki Vesnik, 62(2), 127–136, 2010.
• Frasin, B. A. A note on certain analytic and univalent functions, Southeast Asian J. Math. 28, 829–836, 2004.
• Frasin, B. A. and Ahmad, A -S. Sufficient conditions for univalence of integral operator defined by Hadamard product, Submitted.
• Frasin, B. A. and Darus, M. On certain analytic univalent functions, Internat. J. Math. and Math. Sci. 25 (5), 305–310, 2001.
• Nehari, Z. Conformal Mappings (McGraw-Hill Book Comp., New York, 1952) (Dover. Publ. Inc., 1975).
• Pascu, N. On a univalence criterion, II, Itinerant Seminar on Functional Equations, Approx- imation and Convexity (Cluj-Napoca, 1985), Preprint, 85, Universitatea “Babes-Bolyai”, Cluj-Napoca, 153–154, 1985. [13] Pascu, N. An improvement of Backer’s univalence criterion (Proceedings of the Commem- orative Session Simion Stoilow, Brasov, 1987), 43–48.
• Pescar, V. A new generalization of Ahlfor’s and Becker’s criterion of univalence, Bull. Malaysian Math. Soc. (Second Series) 19, 53–54, 1996.
• Ruscheweyh, St. New criteria for univalent functions, Proc. Amer.Math. Soc. 49 (1), 109– 115, 1975.
• Salagean, G. Subclasses of univalent functions (Lecture Notes in Math. 1013, Springer- Verlag, 1983), 362–372.
• Selvaraj, C. and Karthikeyan, K. R. Sufficient conditions for univalence of a general integral operator, Acta Univ. Apu. 17, 87–94, 2009.