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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
Journal Section Mathematics
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 (June 2013), 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.