In this paper, we introduce and investigate two new subclasses of analytic functions with bounded boundary and bounded radius rotations by using a certain p-valent operator which complies with the known Carlson-Shaffer operator for p = 1. Both of these operators are heavily explored and have various applications. We investigate some inclusions results and integral preserving properties. We also extend the Ruscheweyh and Sheil-Small convolution preserving properties in the context of these classes. We relate our finding with the existing known results found in the literature regarding this subject.
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The object of the present paper is to investigate coefficient estimates and closure theorems for functions belonging to the class R[..] of p-valent prestarlike functions with negative coefficients. We also consider integral operators associalted with functions belonging to the class R[..]. Furthermore, distortion theorems involving a generalized fractional integral (derivative) opertaor for functions in this class are proved.
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