A study on certain inequalities for p-valent functions

Year 2015, Volume: 36 Issue: 3, 512 - 521, 13.05.2015

Roya Ghasemkhani

Abstract

Abstract. In this paper, we derive conditions on the parameters a, b, c so that the function is p-valent starlike and p-valent convex functions in, where  denotes the classical hypergeometric function. We also consider an integral operator related to the hypergeometric function.

Keywords

starlike, convex; p-valent; hypergeometric function

References

• Goodman, A.W. (1991), “On uniformly starlike functions, ”J. Math. Anal. Appl., 155, 364–370.
• Al-kharsani H.A. and Al-Hajiry, S.S. (2006), “Subordination results for the family of uniformly convex p-valent functions,” J. Inequal. Pure and Appl. Math., 7(1), Art. 20. [online: http: //jipam.vu.edu.au/article.php?
• Silverman, H. (1975), “Univalent functions with negative coefficients,” Proc. Amer. Math. Soc. 51, pp. 109-116. [4] Owa, S. (1985), “On certain classes of p-valent functions with negative coefficients,” Bull. Belg. Math. Soc. Simon stevin, 59, pp. 385-402.
• Al-kharsani H.A. and Al-Hajiry, S.S. (2008), “a note on certain inequalities for p-valent functions,” Journal of inequalities in pure and applied mathmatics, vol 9(2008), Issue 3, Article 90, 6pp.
• El-ashwah, R.M., Aouf, M.K. and Moustafa, A. O.(2010), “Starlike and convexity properties for p-valent hypergeometric functions, ” Acta Math. Univ. Comenianae, Vol. LXXIX, 1, pp. 55-64. [7] Chen M.-P., Multivalent functions with negative coe_cients in the unit disc, Tamkang J. Math. 17(3) (1986), 127{137.