## Some families of linear operators associated with certain subclasses of multivalent functions.(English)Zbl 1155.30309

Summary: Making use of a certain linear operator, which is defined here by means of the Hadamard product (or convolution), we introduce two novel subclasses $\mathcal P_{a,c}(A,B; p,\lambda)\qquad \text{and}\qquad \mathcal P^+_{a,c}(A,B; p,\lambda)$ of the class $$\mathcal A(p)$$ of normalized $$p$$-valent analytic functions in the open unit disk. The main objective of the present paper is to investigate the various important properties and characteristics of each of these subclasses. Furthermore, several properties involving neighborhoods of functions in these subclasses are investigated. We also derive many results for the modified Hadamard products of functions belonging to the class $$\mathcal P^+_{a,c}(A,B;p,\lambda)$$. Finally, some applications of fractional calculus operators are considered.

### MSC:

 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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### References:

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