Some subclasses of analytic functions involving certain integral operator. (English) Zbl 1502.30038
Summary: 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.
MSC:
| 30C45 | Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) |
| 30C80 | Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination |
Keywords:
classes of analytic functions; subordination; bounded boundary rotation; bounded radius rotationReferences:
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