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The purpose of this paper is to present a solution to perhaps the final remaining case in the line of study concerning the generalization of Forellis theorem on the complex analyticity of the functions that are: (1) $mathcal{C}^infty$ smooth at a point, and (2) holomorphic along the complex integral curves generated by a contracting holomorphic vector field with an isolated zero at the same point.
In this paper we first prove a version of $L^{2}$ existence theorem for line bundles equipped a singular Hermitian metrics. Aa an application, we establish a vanishing theorem which generalizes the classical Nadel vanishing theorem.
Clunie and Hayman proved that if the spherical derivative of an entire function has order of growth sigma then the function itself has order at most sigma+1. We extend this result to holomorphic curves in projective space of dimension n omitting n hyperplanes in general position.
A motivation comes from {em M. Ismail and et al.: A generalization of starlike functions, Complex Variables Theory Appl., 14 (1990), 77--84} to study a generalization of close-to-convex functions by means of a $q$-analog of a difference operator acti
This note is devoted to two classical theorems: the open mapping theorem for analytic functions (OMT) and the fundamental theorem of algebra (FTA). We present a new proof of the first theorem, and then derive the second one by a simple topological ar
The aim of this research paper is to obtain explicit expressions of (i) $ {}_1F_1 left[begin{array}{c} alpha 2alpha + i end{array} ; x right]. {}_1F_1left[ begin{array}{c} beta 2beta + j end{array} ; x right]$ (ii) ${}_1F_1 left[ begin{array}{c