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Several inclusions between the class of functions with positive real part and the class of starlike univalent functions associated with lemniscate of Bernoulli are obtained by making use of the well-known theory of differential subordination. Further, these inclusions give suficient conditions for normalized analytic functions to belong to some subclasses of starlike functions. The results also provide sharp version of some previously known results. [ABSTRACT FROM AUTHOR]

Abstract: The main purpose of this paper is to establish connections between various subclasses of harmonic mappings in the plane by applying certain convolution operators involving hypergeometric functions. To be more precise, we investigate such connections with harmonic k-uniformly starlike and harmonic k-uniformly convex mappings in the plane. [Copyright &y& Elsevier]

The article discusses the relationship of neighborhoods of starlike and convex functions with parabola. It mentions several mathematicians who introduced additional general notions of neighbourhood of an analytic function. It states that problems related to the neighbourhoods of analytic functions were given consideration and examples are shown through mathematical notation and formulas. The result of the investigation of the geometric properties are also presented through a series of computations.