CONVEXITY OF INTEGRAL OPERATORS OF p -VALENT FUNCTIONS

Year 2012, Volume: 41 Issue: 6, 875 - 881, 01.06.2012

Gülşah Saltık Ayhanöz Ekrem Kadıoğlu

Abstract

CONVEXITY OF INTEGRAL OPERATORS OF p -VALENT FUNCTIONS

Abstract

In this paper, we consider two general p-valent integral operators for certain analytic functions in the unit disc U and give some properties for these integral operators on some classes of univalent functions.

Keywords

Analytic functions, Integral operators, p-valently starlike functions, pvalently convex functions, 2000 AMS Classification: 30 C 45

References

• Alexander, J. W.Functions which map the interior of the unit circle upon simple regions, Annals of Mathematics 17 (1), 12–22, 1915.
• Alb Lupa¸s, A. A subclass of analytic functions defined by differential S˘al˘agean operator, Acta Universitatis Apulensis 20, 259–263, 2009.
• Breaz D. and Breaz, N. Two integral operators, Studia Universitatis Babes-Bolyai Mathe- matica 47 (3), 13–19, 2002.
• Breaz, D., G¨uney, H. ¨O. and S˘al˘agean, G. S. A new general integral operator, Tamsui Oxford Journal of Mathematical Sciences 25 (4), 407–414, 2009.
• Deniz, E., C¸ a˘glar, M. and Orhan, H. The order of convexity of two p-valent integral op- erators, American Institute of Physics, International Symposium of Mathematical Science, Bolu, Turkey, (1309), 234–240, 2010.
• Frasin, B. A. Convexity of integral operators of p-valent functions, Math. Comput. Model. 51, 601–605, 2010.
• Frasin, B. A. and Darus, M. On certain analytic univalent functions, Internat. J. Math. and Math. Sci. 25 (5), 305–310, 2001.
• Frasin, B. A. and Jahangiri, J. A new and comprehensive class of analytic functions, Anal. Univ. Ordea Fasc. Math. XV, 59–62, 2008.
• Frasin, B. A. and Ahmad, A. The order of convexity of two integral operators, Studia Univ. “Babe¸s-Bolyai”, Mathematica LV (2)(6), 113-117, 2010.
• Miller, S. S., Mocanu, P. T. and Reade, M. O. Starlike integral operators, Pacific Journal of Mathematics 79 (1), 157–168, 1978.
• Pescar V. and Owa, S. Sufficient conditions for univalence of certain integral operators, Indian Journal of Mathematics 42 (3), 347–351, 2000.
• S˘al˘agean, G. St. Subclases of univalent functions (Lecture Notes in Math., Springer Verlag, Berlin, 1983), 362–372.
• Saltık, G., Deniz E., and Kadıo˘glu, E. Two new general p-valent integral operators, Math. Comput. Model. 52, 1605–1609, 2010.
• Shenan, G. M., Salim, T. O. and Marouf, M. S. A certain class of multivalent prestar- like functions involving the Srivastava-Saigo-Owa fractional integral operator, Kyungpook Math. J. 44, 353–362, 2004.