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On the univalence of an integral operator

Yıl 2015, Cilt: 44 Sayı: 3, 623 - 631, 01.06.2015

Öz

In this paper the method of Loewner chains is used to derive a fairly general and flexible univalence criterion for an integral operator. Two examples involving Bessel and hypergeometric functions are given. Our results include a number of known or new univalence criteria.

Kaynakça

  • [1] L. V. Ahlfors,Sufficient conditions for quasiconformal extension, Ann. Math. Studies., 79 (1974), 23-29.
  • [2] A. Baricz, B. A. Frasin ,Univalence of integral operator involving Bessel functions, Appl. Math. Lett., 23(4)(2010), 371-376.
  • [3] J. Becker, Löwnersche differential gleichung und quasikonform fortsetzbare schlichte functionen, J. Reine Angew. Math.255 (1972), 23-43.
  • [4] J. Becker, Conformal mappings with quasiconformal extensions, Aspects of Contemporary Complex Analysis, Ed. by D. A. Brannan and J. G. Clunie, Acad. Press, 1980, 37-77.
  • [5] D. Breaz, N. Breaz, H. M. Srivastava, An extension of the univalent condition for a family of integral operators, Appl. Math. Lett., 22(2009), 41-44.
  • [6] E. Deniz, H. Orhan, H. M. Srivastava, Some sufficient conditions for univalence of certain families of integral operators involving generalized Bessel functions, Taiwanese J. Math., 15(2)(2011), 883-971.
  • [7] E. Deniz, D. Raducanu, H. Orhan, On the univalence of an integral operator defined by Hadamard product, Appl. Math. Lett., 25(2012), 179-184.
  • [8] B. A. Frasin, Certain sufficient conditions for univalence of two integral operators, European J. Pure Appl. Math., 3(6)(2010), 1141-1149.
  • [9] S. Moldoveanu, N. N. Pascu, Integral operators which preserve the univalence, Mathematica (Cluj), 32(55)(1990), 159-166.
  • [10] H. Ovesea, An extension of Lewandowski’s univalence criterion, Demonstratio Math., XXIX, 4(1996), 699-706.
  • [11] H. Ovesea, A generalization of Ruscheweyh’s univalence criterion, J. Math. Anal. Appl., 258 (2001), 102-109.
  • [12] N. N. Pascu, An improvement of Becker’s univalence criterion, Commemorative Session Simion Stoilov, Univ. of Brasov, (Preprint) (1987), 43-48.
  • [13] V. Pescar, A new generalization of Ahlfors and Becker’s criterion of univalence, Bull. Math. Malaysian Math. Soc. (Second Series), 19 (1996), 53-54.
  • [14] V. Pescar, D. Breaz, The Univalence of Integrals Operators, Prof. M. Drinov Acad. Publish. House, Sofia, 2008.
  • [15] Ch. Pommerenke, Über die Subordination analytischer Funktionen, J. Reine Angew Math., 218 (1965), 159-173.
  • [16] Ch. Pommerenke, Univalent Functions, Vandenhoeck Ruprecht in Göttingen, 1975.
  • [17] D. Raducanu, H. Orhan, E. Deniz, On some sufficient conditions for univalence, An. St. Univ. Ovidius, Constanµa, Ser. Math., 18(2)(2010), 217-222.
  • [18] H. M. Srivastava, E. Deniz, H. Orhan, Some general univalence criteria for a family of integral operators, Appl. Math. Comp., 215(2010), 3696-3701.
  • [19] D. Tan, Quasiconformal extension and univalency criteria, Mich. Math. J., 39(1992), 163- 172.
Yıl 2015, Cilt: 44 Sayı: 3, 623 - 631, 01.06.2015

Öz

Kaynakça

  • [1] L. V. Ahlfors,Sufficient conditions for quasiconformal extension, Ann. Math. Studies., 79 (1974), 23-29.
  • [2] A. Baricz, B. A. Frasin ,Univalence of integral operator involving Bessel functions, Appl. Math. Lett., 23(4)(2010), 371-376.
  • [3] J. Becker, Löwnersche differential gleichung und quasikonform fortsetzbare schlichte functionen, J. Reine Angew. Math.255 (1972), 23-43.
  • [4] J. Becker, Conformal mappings with quasiconformal extensions, Aspects of Contemporary Complex Analysis, Ed. by D. A. Brannan and J. G. Clunie, Acad. Press, 1980, 37-77.
  • [5] D. Breaz, N. Breaz, H. M. Srivastava, An extension of the univalent condition for a family of integral operators, Appl. Math. Lett., 22(2009), 41-44.
  • [6] E. Deniz, H. Orhan, H. M. Srivastava, Some sufficient conditions for univalence of certain families of integral operators involving generalized Bessel functions, Taiwanese J. Math., 15(2)(2011), 883-971.
  • [7] E. Deniz, D. Raducanu, H. Orhan, On the univalence of an integral operator defined by Hadamard product, Appl. Math. Lett., 25(2012), 179-184.
  • [8] B. A. Frasin, Certain sufficient conditions for univalence of two integral operators, European J. Pure Appl. Math., 3(6)(2010), 1141-1149.
  • [9] S. Moldoveanu, N. N. Pascu, Integral operators which preserve the univalence, Mathematica (Cluj), 32(55)(1990), 159-166.
  • [10] H. Ovesea, An extension of Lewandowski’s univalence criterion, Demonstratio Math., XXIX, 4(1996), 699-706.
  • [11] H. Ovesea, A generalization of Ruscheweyh’s univalence criterion, J. Math. Anal. Appl., 258 (2001), 102-109.
  • [12] N. N. Pascu, An improvement of Becker’s univalence criterion, Commemorative Session Simion Stoilov, Univ. of Brasov, (Preprint) (1987), 43-48.
  • [13] V. Pescar, A new generalization of Ahlfors and Becker’s criterion of univalence, Bull. Math. Malaysian Math. Soc. (Second Series), 19 (1996), 53-54.
  • [14] V. Pescar, D. Breaz, The Univalence of Integrals Operators, Prof. M. Drinov Acad. Publish. House, Sofia, 2008.
  • [15] Ch. Pommerenke, Über die Subordination analytischer Funktionen, J. Reine Angew Math., 218 (1965), 159-173.
  • [16] Ch. Pommerenke, Univalent Functions, Vandenhoeck Ruprecht in Göttingen, 1975.
  • [17] D. Raducanu, H. Orhan, E. Deniz, On some sufficient conditions for univalence, An. St. Univ. Ovidius, Constanµa, Ser. Math., 18(2)(2010), 217-222.
  • [18] H. M. Srivastava, E. Deniz, H. Orhan, Some general univalence criteria for a family of integral operators, Appl. Math. Comp., 215(2010), 3696-3701.
  • [19] D. Tan, Quasiconformal extension and univalency criteria, Mich. Math. J., 39(1992), 163- 172.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Dorina Raducanu Bu kişi benim

Yayımlanma Tarihi 1 Haziran 2015
Yayımlandığı Sayı Yıl 2015 Cilt: 44 Sayı: 3

Kaynak Göster

APA Raducanu, D. (2015). On the univalence of an integral operator. Hacettepe Journal of Mathematics and Statistics, 44(3), 623-631.
AMA Raducanu D. On the univalence of an integral operator. Hacettepe Journal of Mathematics and Statistics. Haziran 2015;44(3):623-631.
Chicago Raducanu, Dorina. “On the Univalence of an Integral Operator”. Hacettepe Journal of Mathematics and Statistics 44, sy. 3 (Haziran 2015): 623-31.
EndNote Raducanu D (01 Haziran 2015) On the univalence of an integral operator. Hacettepe Journal of Mathematics and Statistics 44 3 623–631.
IEEE D. Raducanu, “On the univalence of an integral operator”, Hacettepe Journal of Mathematics and Statistics, c. 44, sy. 3, ss. 623–631, 2015.
ISNAD Raducanu, Dorina. “On the Univalence of an Integral Operator”. Hacettepe Journal of Mathematics and Statistics 44/3 (Haziran 2015), 623-631.
JAMA Raducanu D. On the univalence of an integral operator. Hacettepe Journal of Mathematics and Statistics. 2015;44:623–631.
MLA Raducanu, Dorina. “On the Univalence of an Integral Operator”. Hacettepe Journal of Mathematics and Statistics, c. 44, sy. 3, 2015, ss. 623-31.
Vancouver Raducanu D. On the univalence of an integral operator. Hacettepe Journal of Mathematics and Statistics. 2015;44(3):623-31.