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CHARACTERIZATION PROPERTIES FORSTARLIKENESS AND CONVEXITY OF SOMESUBCLASSES OF P-VALENT FUNCTIONSINVOLVING A CLASS OF INTEGRALOPERATORS

Year 2013, Volume: 42 Issue: 6, 599 - 604, 01.06.2013

Abstract

This paper studies the sufficient conditions for the starlikeness andconvexity of a class of fractional integral operators of certain analyticand p-valent functions in the open unit disk. Further characterizationtheorems associated with the Hadamard product (or convolution) arealso considered.

References

  • Goodman, A. W. On the Shwarz-Christoffel transformation and p-valent functions, Trans. Amer. Math. Soc. 68, 204-223, 1950.
  • Kapoor, G. P. and Mishra, A. K. Convex hulls and extreme points of some classes of multivalent functions, J. Math. Anal. Appl. 87(1), 116-126, 1982.
  • Owa, S. On certain classes of p-valent functions with negative coefficients, Bull. Belg. Math. Soc. Simon Stevin 59, 385-402, 1985.
  • Owa, S., Saigo, M. and Srivastava, H. M. Some characterization theorems for starlike and convex functions involving a certain fractional integral operator, J. Math. Anal. Appl. 140, 419-426, 1989.
  • Partil, D. A. and Thakare, N. K. On convex hulls and extreme points of p-valent starlike and convex classes with applications, Bull. Math. Soc. Sci. Math. R. S. Roumanie (N. S.) 27, 145-160, 1983.
  • Raina, R. K. and Bolia, M. Characterization properties for starlike and convex functions involving a class of fractional integral operators, Rend. Sem. Mat. Univ. Padova. 97, 61-71, 19 Robertson, M. S. On the theory of univalent functions, Ann. Math. 37, 374-408, 1936. Ruscheweyh, S. and Sheil-Small, T. Hadamard products of schlicht functions and the PolyaSchoenberg conjecture, comment Math. Helv. 48, 119-135, 1973.
  • Silverman, H. Univalent functions with negative coefficients, Proc. Amer. Math. Soc. 51, 109-116, 1975.
  • Srivastava, H. M. and Karlsson, P. M. Multiple Gaussian hypergeometric series, (Halsted Press, Ellis Horwood Limited, Chichester, Wiley, New York/ Chichester/ Brishane/ Toronto, 1985).
  • Srivastava, H. M., Saigo, M. and Owa, S. A class of distortion theorems involving certain operators of fractional calculus, J. Math. Anal. Appl. 131, 412-420, 1988.

CHARACTERIZATION PROPERTIES FORSTARLIKENESS AND CONVEXITY OF SOMESUBCLASSES OF P-VALENT FUNCTIONSINVOLVING A CLASS OF INTEGRALOPERATORS

Year 2013, Volume: 42 Issue: 6, 599 - 604, 01.06.2013

Abstract

-

References

  • Goodman, A. W. On the Shwarz-Christoffel transformation and p-valent functions, Trans. Amer. Math. Soc. 68, 204-223, 1950.
  • Kapoor, G. P. and Mishra, A. K. Convex hulls and extreme points of some classes of multivalent functions, J. Math. Anal. Appl. 87(1), 116-126, 1982.
  • Owa, S. On certain classes of p-valent functions with negative coefficients, Bull. Belg. Math. Soc. Simon Stevin 59, 385-402, 1985.
  • Owa, S., Saigo, M. and Srivastava, H. M. Some characterization theorems for starlike and convex functions involving a certain fractional integral operator, J. Math. Anal. Appl. 140, 419-426, 1989.
  • Partil, D. A. and Thakare, N. K. On convex hulls and extreme points of p-valent starlike and convex classes with applications, Bull. Math. Soc. Sci. Math. R. S. Roumanie (N. S.) 27, 145-160, 1983.
  • Raina, R. K. and Bolia, M. Characterization properties for starlike and convex functions involving a class of fractional integral operators, Rend. Sem. Mat. Univ. Padova. 97, 61-71, 19 Robertson, M. S. On the theory of univalent functions, Ann. Math. 37, 374-408, 1936. Ruscheweyh, S. and Sheil-Small, T. Hadamard products of schlicht functions and the PolyaSchoenberg conjecture, comment Math. Helv. 48, 119-135, 1973.
  • Silverman, H. Univalent functions with negative coefficients, Proc. Amer. Math. Soc. 51, 109-116, 1975.
  • Srivastava, H. M. and Karlsson, P. M. Multiple Gaussian hypergeometric series, (Halsted Press, Ellis Horwood Limited, Chichester, Wiley, New York/ Chichester/ Brishane/ Toronto, 1985).
  • Srivastava, H. M., Saigo, M. and Owa, S. A class of distortion theorems involving certain operators of fractional calculus, J. Math. Anal. Appl. 131, 412-420, 1988.
There are 9 citations in total.

Details

Primary Language Turkish
Authors

Somia Muftah Amsheri This is me

Valentina Zharkova This is me

Publication Date June 1, 2013
Published in Issue Year 2013 Volume: 42 Issue: 6

Cite

APA Amsheri, S. M., & Zharkova, V. (2013). CHARACTERIZATION PROPERTIES FORSTARLIKENESS AND CONVEXITY OF SOMESUBCLASSES OF P-VALENT FUNCTIONSINVOLVING A CLASS OF INTEGRALOPERATORS. Hacettepe Journal of Mathematics and Statistics, 42(6), 599-604.
AMA Amsheri SM, Zharkova V. CHARACTERIZATION PROPERTIES FORSTARLIKENESS AND CONVEXITY OF SOMESUBCLASSES OF P-VALENT FUNCTIONSINVOLVING A CLASS OF INTEGRALOPERATORS. Hacettepe Journal of Mathematics and Statistics. June 2013;42(6):599-604.
Chicago Amsheri, Somia Muftah, and Valentina Zharkova. “CHARACTERIZATION PROPERTIES FORSTARLIKENESS AND CONVEXITY OF SOMESUBCLASSES OF P-VALENT FUNCTIONSINVOLVING A CLASS OF INTEGRALOPERATORS”. Hacettepe Journal of Mathematics and Statistics 42, no. 6 (June 2013): 599-604.
EndNote Amsheri SM, Zharkova V (June 1, 2013) CHARACTERIZATION PROPERTIES FORSTARLIKENESS AND CONVEXITY OF SOMESUBCLASSES OF P-VALENT FUNCTIONSINVOLVING A CLASS OF INTEGRALOPERATORS. Hacettepe Journal of Mathematics and Statistics 42 6 599–604.
IEEE S. M. Amsheri and V. Zharkova, “CHARACTERIZATION PROPERTIES FORSTARLIKENESS AND CONVEXITY OF SOMESUBCLASSES OF P-VALENT FUNCTIONSINVOLVING A CLASS OF INTEGRALOPERATORS”, Hacettepe Journal of Mathematics and Statistics, vol. 42, no. 6, pp. 599–604, 2013.
ISNAD Amsheri, Somia Muftah - Zharkova, Valentina. “CHARACTERIZATION PROPERTIES FORSTARLIKENESS AND CONVEXITY OF SOMESUBCLASSES OF P-VALENT FUNCTIONSINVOLVING A CLASS OF INTEGRALOPERATORS”. Hacettepe Journal of Mathematics and Statistics 42/6 (June2013), 599-604.
JAMA Amsheri SM, Zharkova V. CHARACTERIZATION PROPERTIES FORSTARLIKENESS AND CONVEXITY OF SOMESUBCLASSES OF P-VALENT FUNCTIONSINVOLVING A CLASS OF INTEGRALOPERATORS. Hacettepe Journal of Mathematics and Statistics. 2013;42:599–604.
MLA Amsheri, Somia Muftah and Valentina Zharkova. “CHARACTERIZATION PROPERTIES FORSTARLIKENESS AND CONVEXITY OF SOMESUBCLASSES OF P-VALENT FUNCTIONSINVOLVING A CLASS OF INTEGRALOPERATORS”. Hacettepe Journal of Mathematics and Statistics, vol. 42, no. 6, 2013, pp. 599-04.
Vancouver Amsheri SM, Zharkova V. CHARACTERIZATION PROPERTIES FORSTARLIKENESS AND CONVEXITY OF SOMESUBCLASSES OF P-VALENT FUNCTIONSINVOLVING A CLASS OF INTEGRALOPERATORS. Hacettepe Journal of Mathematics and Statistics. 2013;42(6):599-604.