East Asian mathematical journal

  • 제25권2호
  • /
  • Pages.127-140
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  • 2009
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  • 1226-6973(pISSN)
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  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
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SUBORDINATION RESULTS FOR CERTAIN CLASSES OF MULTIVALENTLY ANALYTIC FUNCTIONS WITH A CONVOLUTION STRUCTURE

  • 투고 : 2000.08.16
  • 심사 : 2000.11.20
  • 발행 : 2009.06.30
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초록

In this paper a general class of analytic functions involving a convolution structure is introduced. Among the results investigated are the various results depicting useful properties and characteristics of this function class by employing the techniques of differential subordination. Relevances of the main results with some known results are also mentioned briefly.

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참고문헌

  1. Abramowitz, M. and Stegun, I. A.(Editors), Handbook of Mathematical Functions and Formulas, Graphs and Mathematical Tables, Dover Publications, New York, 1971.
  2. Aghalary, R., Joshi, S. B., Mohapatra, R. N. and Ravichandran, V., Subordinations for analytic functions defined by Dziok-Srivastava linear operator, Appl. Math. Comput., 37 (2006), 533-542.
  3. Bernardi, S. D., Convex and starlike univalent functions, Trans. Amer. Math. Soc., 135 (1969), 429-446. https://doi.org/10.1090/S0002-9947-1969-0232920-2
  4. Dinggong, Y. and Liu, J. L., On a class of analytic functions involving Ruscheweyh derivatives, Bull. Korean Math. Soc., 39(1) (2002), 123-131. https://doi.org/10.4134/BKMS.2002.39.1.123
  5. Dziok, J. and Raina, R. K., Families of analytic functions associated with the Wright generalized hypergeometric functions, Demonstratio Math., 37 (2004), 533-542.
  6. Dziok, J., Raina, R. K. and Srivastava, H. M., Some classes of analytic functions associated with operator on Hilbert space involving Wright's generalized hypergeometric functions, Proc. Janggeon Math. Soc., 7 (2004), 43-55.
  7. Dziok, J. and Srivastava, H. M., Classes of analytic functions associated with the generalized hypergeometric functions, Appl. Math. Comput., 103 (1999), 1-13. https://doi.org/10.1016/S0096-3003(98)10042-5
  8. Liu, J. L., On subordination for certain multivalent analytic functions associated with the generalized hypergeometric function, J. Inequal. Pure Appl. Math., 7(4) (Article 131)(2006), 1-6 (electronic).
  9. Livingston, A. E., On the radius of the univalence of certain analytic functions, Proc. Amer. Math. Soc., 17 (1966), 352-357. https://doi.org/10.1090/S0002-9939-1966-0188423-X
  10. Miller S. S. and Mocanu P. T., Differential Subordinates: Theory and Applications, Series in Pure and Applied Mathematics, No. 225, Marcel Dekker, New York, (2000).
  11. Miller, S. S. and Mocanu, P. T., Differential subordinations and univalent functions, Michigan Math. J., 28 (1981), 157-171. https://doi.org/10.1307/mmj/1029002507
  12. Obradovic, M., On certain inequalities for some regular functions in ${\left|}z{\right|}$, Int. J. Math. Sci., 8 (1985), 671-678.
  13. Ozkan, O., Some subordination results on multivalent functions defined by integral operator, J. Inequal. Appl., Volume 2007(2007), Article ID 71616, 1-8 (electronic).
  14. R. K. Raina Some results associated with fractional calculus operators involving Appell hypergeometric function, J. Inequal. Pure Appl. Math., 10 (2009), 1-7 (electronic).
  15. Sham, S., Kulkurni, S. R. and Jahangiri, J. M., Subordination properties of pvalent functions defined by integral operators, Internat. J. Math. Math. Sci., Volume 2006(2006), Article ID 94572, 1-3 (electronic).
  16. Srivastava, H. M., Patel, J. and Mohapatra, G. P., Some applications of differential subordination to a general class of multivalent functions, Adv. Stud. Contemp. Math., 3(1) (2001), 1-15.
  17. Srivastava, H. M., Patel, J. and Mohapatra, G. P., A certain class of p-valently analytic functions, Math. Comput. Modelling, 41 (2005), 321-324. https://doi.org/10.1016/j.mcm.2003.06.010
  18. Srivastava, H. M., Suchithra, K., Stephen, B. A. and Sivasubramanian, S., Inclusion and neighborhood properties of certain subclasses of analytic and multivalent functions of complex order, J. Inequal. Pure Appl. Math., 7(5) (Article 191)(2006), 1-8 (electronic).