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Differential subordinations and superordinations for p-valent functions defined by fractional derivative operator

Amsheri S. M., Zharkova V.

Demonstratio Mathematica

2013

Vol. 46, nr 3

503--512

In the present paper, we derive some subordination and superordination results for p-valent functions in the open unit disk by using certain fractional derivative operator. Relevant connections of the results, which are presented in the paper, with various known results are also considered.

Application of generalized Ruscheweyh derivatives on p-valent functions

Parihar H. S., Agarwal R.

Journal of Mathematics and Applications

2011

Vol. 34

75--86

In this paper, we define a new class of p-valent analytic functions with finitely many coefficients by making use of the generalized Ruscheweyh derivatives involving a general fractional derivative operator. Some properties of this class are also investigated. e.g. Coefficient estimates, convex combination, arithmatic mean, extreme points, radii of starlikeness and convexity. Many known results are as a special case of our results.