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

Somia Muftah Amsheri Valentina Zharkova

https://izlik.org/JA66KM65AD

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.

Keywords

p-valent function , starlike function , convex function , fractional integraloperators , Hadamard product.

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

https://izlik.org/JA66KM65AD

Abstract

-

Keywords

-

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.