On alpha-Quasi-Uniformly convex p-valent functions of type $beta$ in terms of Ruscheweyh derivatives

On alpha-Quasi-Uniformly convex p-valent functions of type $beta$ in terms of Ruscheweyh derivatives

In the present paper we will establish some properties of the class of $alpha$ - Quasi - Uniformly convex, p-valent functions of type $beta$ in the open unit disk, which we denote by $QUCV^{p,lambda}_{beta,alpha}$, for $lambda>-1; 0 leqbeta< p, alphageq 0 $ and $pinBbb{N,}$ by making use of the Ruscheweyh Derivatives.

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  • [1] Goodman,A. W. On uniformly convex functions, Annals Polonici Mathematici XVI (1), 8—22, 1991.
  • [2} Khalida, I. On Quasi-convex functions, Car. J. Math. 3, 1-8, 1984.
  • [3] Libera, R. J. Some classes of regular functions, Proc. Amer. Math. Soc. 16, 755-758, 1965.
  • [4] Livingston, A. E. On the radius of univalence of certain analytic functions, Proc. Amer.Math. Soc. 16, 352-357, 1965.
  • [5] Padmanabhan, K.S. On certain sub-classes of Bezilevic functions, Indian J. Math. 9(3),1-16, 1997.
  • [6] Rajagopal, R. and Selvaraj, C. On a class of uniformly quasi-convex functions, Bull. Cal.Math. Soc. 95 (1), 2003.
  • [7] Ronning, F. On starlike functions associated with parabolic regions, Ann. Univ. Marie Curie, Sklo, Sect. A 45, 117-122, 1991.
  • [8] Selvaraj, C. On Alpha - Quasi - Uniformly convex functions, J. of Indian Acad. Math.25(1), 169-185, 2003.