DOI QR코드

DOI QR Code

MULTIPLIER TRANSFORMATIONS AND STRONGLY CLOSE-TO-CONVEX FUNCTIONS

  • Cho, Nak-Eun (Department of Applied Mathematics, Pukyong National University) ;
  • Kim, Tae-Hwa (Department of Applied Mathematics, Pukyong National University)
  • Published : 2003.08.01

Abstract

The purpose of the present paper is to introduce some new subclasses of strongly close-to-convex functions in the open unit disk defined by multiplier transformations and study their properties. Our results include several previous known results as special cases.

Keywords

subordinate;multiplier transformation;strongly close-to-convex;integral operator

References

  1. Trans. Amer. Math. Soc. v.135 Convex and starlike univalent functions S.D.Bernardi https://doi.org/10.2307/1995025
  2. Studia Univ. Babes-Bolyai Mathematica v.34 Alpha-convex integral operators and strongly starlike functions P.T.Mocanu
  3. Lecture Notes in Math. v.1013 Subclasses of univalent functions G.S.Salagean https://doi.org/10.1007/BFb0066543
  4. J. Math. Anal. Appl. v.112 Properties of close-to-convexity preserved by some integral operators K.I.Noor;H.A.Alkhorasani https://doi.org/10.1016/0022-247X(85)90260-4
  5. Internat. J. Math. Math. Sci. v.10 On quasiconvex functions and related topics K.I.Noor https://doi.org/10.1155/S0161171287000310
  6. Distortion theorems in relation to linear integral operators Y.Komatu
  7. Canad. J. Math. v.37 Subclasses of starlike functions subordinate to convex functions H.Silverman;E.M.Silvia https://doi.org/10.4153/CJM-1985-004-7
  8. Proc. Amer. Math. Soc. v.36 On a class of close-to convex schlicht functions H.Silverman https://doi.org/10.1090/S0002-9939-1972-0313494-X
  9. Bull. Acad. Polon. Sci. Sёr. Sci. Math.Astronom. Phys. v.21 Some extremal problems for certain families of analytic functions W.Janowski
  10. Proc. Japan. Acad. Ser. A. Math. Sci. v.69 On the order of strongly starlikeness of strongly convex functions M.Nunokawa https://doi.org/10.3792/pjaa.69.234
  11. General Inequalities v.3 On a Briot-Bouquet differential subordination P.Eenigenburg;S.S.Miller;P.T.Mocanu;M.O.Reade
  12. J. Math. Anal. Appl. v.261 The Noor integral and strongly starlike functions J.Liu https://doi.org/10.1006/jmaa.2001.7489
  13. Current topics in analytic function theory H.M.Srivastava;S.Owa(ed.)
  14. Trans. Amer. Math. Soc. v.114 On close-to-convex analytic functions Ch.Pommerenke https://doi.org/10.1090/S0002-9947-1965-0174720-4
  15. Michigan Math. J. v.28 Differential subordinations ans univalent functions S.S.Miller;P.T.Mocanu https://doi.org/10.1307/mmj/1029002507
  16. Proc. Amer. Math. Soc. v.16 Some classes of regular univalent functions R.J.Libera https://doi.org/10.1090/S0002-9939-1965-0178131-2

Cited by

  1. Main differential sandwich theorem with some applications vol.30, pp.1, 2009, https://doi.org/10.1134/S1995080209010016
  2. Majorization for certain classes of analytic functions using multiplier transformation vol.23, pp.5, 2010, https://doi.org/10.1016/j.aml.2010.01.029
  3. Inclusion properties of a subclass of analytic functions defined by an integral operator involving the Gauss hypergeometric function vol.218, pp.7, 2011, https://doi.org/10.1016/j.amc.2011.09.026
  4. On Certain Classes ofp-Valent Functions by Using Complex-Order and Differential Subordination vol.2010, 2010, https://doi.org/10.1155/2010/275935
  5. Some Inclusion Relationships of Certain Subclasses of -Valent Functions Associated with a Family of Integral Operators vol.2013, 2013, https://doi.org/10.1155/2013/384170
  6. On special strong differential subordinations using multiplier transformation vol.25, pp.3, 2012, https://doi.org/10.1016/j.aml.2011.09.074
  7. Some properties of a subclass of harmonic univalent functions defined by the multiplier transformations vol.46, pp.3, 2015, https://doi.org/10.1007/s13226-015-0132-9
  8. Differential Subordinations Associated with Multiplier Transformations vol.2008, 2008, https://doi.org/10.1155/2008/845724
  9. A Study on Becker's Univalence Criteria vol.2011, 2011, https://doi.org/10.1155/2011/759175
  10. Differential sandwich results for certain subclasses of analytic functions vol.54, pp.1-2, 2011, https://doi.org/10.1016/j.mcm.2011.03.028
  11. On integral operators for certain classes of p-valent functions associated with generalized multiplier transformations vol.22, pp.1, 2014, https://doi.org/10.1016/j.joems.2013.06.007
  12. A new comprehensive class of analytic functions defined by multiplier transformation vol.54, pp.9-10, 2011, https://doi.org/10.1016/j.mcm.2011.05.044
  13. Certain subclasses of multivalent analytic functions defined by multiplier transforms vol.216, pp.1, 2010, https://doi.org/10.1016/j.amc.2010.01.031
  14. On differential sandwich theorems for some subclasses of analytic functions associated with multiplier transformation vol.53, pp.9, 2008, https://doi.org/10.1080/17476930802193307
  15. The generalization of the generalized Al-Oboudi differential operator vol.215, pp.4, 2009, https://doi.org/10.1016/j.amc.2009.06.021
  16. Subordination results for certain class of analytic functions defined by convolution vol.60, pp.1-2, 2011, https://doi.org/10.1007/s12215-011-0048-0
  17. Differential subordination and superordination for certain subclasses of p-valent functions vol.51, pp.5-6, 2010, https://doi.org/10.1016/j.mcm.2009.12.027
  18. On differential sandwich theorems of analytic functions defined by certain linear operator vol.64, pp.2, 2010, https://doi.org/10.2478/v10062-010-0009-7
  19. Majorization for A Subclass ofβ-Spiral Functions of OrderαInvolving a Generalized Linear Operator vol.2011, 2011, https://doi.org/10.1155/2011/167672
  20. A unified class of analytic functions with negative coefficients vol.29, pp.3, 2008, https://doi.org/10.1134/S1995080208030086
  21. Subordination and superordination preserving properties for generalized multiplier transformation operator vol.55, pp.3-4, 2012, https://doi.org/10.1016/j.mcm.2011.10.024
  22. On sandwich theorems for certain subclasses of non-Bazilevič functions involving Cho–Kim transformation‖ vol.52, pp.10-11, 2007, https://doi.org/10.1080/17476930701552223
  23. Some Properties of Certain Multivalent Analytic Functions Involving the Cătas Operator vol.2011, 2011, https://doi.org/10.1155/2011/752341
  24. A new class defined by subordination for γ-spirallike functions vol.24, pp.3, 2016, https://doi.org/10.1016/j.joems.2015.08.005
  25. Subordination Properties of Multivalent Functions Defined by Generalized Multiplier Transformation vol.2014, 2014, https://doi.org/10.1155/2014/187482
  26. Applications of Fractionalq-Calculus to Certain Subclass of Analyticp-Valent Functions with Negative Coefficients vol.2015, 2015, https://doi.org/10.1155/2015/273236
  27. Differential sandwich theorems for multivalent functions vol.62, pp.1, 2008, https://doi.org/10.2478/v10062-008-0001-7
  28. On Subclass of -Uniformly Convex Functions of Complex Order Involving Multiplier Transformations vol.2012, 2012, https://doi.org/10.1155/2012/150571
  29. A NEW SUBCLASS OF ANALYTIC FUNCTIONS DEFINED BY CONVOLUTION vol.19, pp.4, 2011, https://doi.org/10.11568/kjm.2011.19.4.351
  30. Some properties of certain classes of p-valent functions defined by the hadamard product vol.48, pp.6, 2013, https://doi.org/10.3103/S106836231306006X
  31. On a class of multivalent functions defined by an extended multiplier transformations vol.60, pp.3, 2010, https://doi.org/10.1016/j.camwa.2010.05.008
  32. Differential Sandwich Theorems for Analytic Functions Defined by an Extended Multiplier Transformation vol.02, pp.05, 2012, https://doi.org/10.4236/apm.2012.25045
  33. Certain Subclasses of Multivalent Functions Defined by New Multiplier Transformations vol.36, pp.6, 2011, https://doi.org/10.1007/s13369-011-0103-3
  34. Class of Multivalent Analytic Functions Defined by a Linear Operator vol.2013, 2013, https://doi.org/10.1155/2013/509717
  35. Sandwich theorems for p-valent functions defined by a certain integral operator vol.53, pp.9-10, 2011, https://doi.org/10.1016/j.mcm.2010.12.030
  36. On a certain class of analytic functions associated with a convolution structure vol.41, pp.3, 2008, https://doi.org/10.1515/dema-2013-0107
  37. On Certain p-Valent Analytic Functions Involving a Linear Operator and Majorization Problems vol.42, pp.1, 2014, https://doi.org/10.1007/s10013-013-0029-z
  38. SOME INCLUSION RELATIONSHIPS ASSOCIATED WITH A CERTAIN CLASS OF INTEGRAL OPERATORS vol.03, pp.04, 2010, https://doi.org/10.1142/S1793557110000519
  39. Differential Subordination Results for Certain Integrodifferential Operator and Its Applications vol.2012, 2012, https://doi.org/10.1155/2012/638234
  40. Inclusion properties of certain subclass of analytic functions defined by multiplier transformations vol.63, pp.1, 2009, https://doi.org/10.2478/v10062-009-0003-0