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Higher order uniformly close-to-convex functions

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  • In this paper, we define and study some subclasses of analytic functions related with $k$-uniformly close-to-convex functions of higher order in the unit disc. These classes unify a number of classes previously studied. The results obtained include rate of growth of coefficients, inclusion relations, radius problems and necessary conditions for univalency. We derive many known results as special cases.
    Mathematics Subject Classification: 30C45, 30A10, 30C50.


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