Differential subordinations obtained by using a fractional operator
DOI:
https://doi.org/10.24193/subbmath.2018.4.05Keywords:
differential subordination, analytic function, fractional operator, convex functionAbstract
We investigate several differential subordinations using the fractional operator $\mathbb{D}_\lambda^{\nu, n}:\mathcal{A}\to\mathcal{A}$, for $-\infty<\lambda<2, \nu>-1, n\in\mathbb{N}_0=\{0,1,2,...\}$, introduced in \cite{7}.References
S. S. Miller, P. T. Mocanu,
Differential Subordinations: Theory and Applications, Pure and Applied Mathematics No. 225, Marcel Dekker, New York, 2000.
S. S. Miller, P. T. Mocanu,
On some classes of first order differential subordinations, Michigan Math. J., 32(1985), 185-195.
S. Owa,
On the distortion theorems I, Kyungpook Math. J., 18(1978), 53-59.
S. Owa, H. M. Srivastava,
Univalent and starlike generalized hypergeometric functions, Canad. J. Math., 39(1987), 1057-1077.
St. Ruscheweyh,
New criteria for univalent functions, Proc. Amer. Math. Soc., 49(1975), 109-115.
G. Ş. Sălăgean,
Subclasses of univalent functions, Lecture Notes in Math. (Springer Verlag), 1013(1983), 362-372.
P. Sharma, R. K. Raina, G. Ş. Sălăgean,
Some Geometric Properties of Analytic Functions Involving a new Fractional Operator, Mediterr. J. Math., 13(2016), 4591-4605.
E. Szatmari,
On a class of analytic functions defined by a fractional operator, submitted
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