On extreme points and product properties of a new subclass of \(p\)-harmonic functions. (English) Zbl 1499.31002
Summary: In this paper, we introduce a new subclass of \(p\)-harmonic functions and investigate the univalence and sense-preserving, extreme points, distortion bounds, convex combination, neighborhoods of mappings belonging to the subclass. Relevant connections of the results presented here with the results of previous research are briefly indicated. Finally, we also prove new properties of the Hadamard product of these classes.
MSC:
| 31A05 | Harmonic, subharmonic, superharmonic functions in two dimensions |
| 31A30 | Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions |
| 30C50 | Coefficient problems for univalent and multivalent functions of one complex variable |
| 30C55 | General theory of univalent and multivalent functions of one complex variable |
Keywords:
analytic function; \(p\)-harmonic functions; extreme points; neighborhood; Hadamard productReferences:
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