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On a subclass of uniformly convex functions defined by the Dziok-Srivastava operator. (English) Zbl 1375.30011

Summary: Making use of the Dziok-Srivastava operator, we define a new subclass \(T^{l}_{m}([\alpha _{1}];\alpha ,\beta )\) of uniformly convex functions with negative coefficients. In this paper, we obtain coefficient estimates, distortion theorems, locate extreme points and obtain radii of close-to-convexity, starlikeness and convexity for functions belonging to the class \(T^{l}_{m}([\alpha _{1}];\alpha ,\beta )\). We consider integral operators associated with functions belonging to the class \(H^{l}_{m}([\alpha _{1}];\alpha ,\beta )\) defined via the Dziok-Srivastava operator. We also obtain several results for the modified Hadamard products of functions belonging to the class \(T^{l}_{m}([\alpha _{1}];\alpha ,\beta )\) and we obtain properties associated with generalized fractional calculus operators.

MSC:

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