Open AccessOn some properties of p-holomorphic and p-analytic function
Author(s) -
I. L. Vassilyev,
V. V. Dovgodilin
Publication year - 2021
Publication title -
vescì nacyânalʹnaj akadèmìì navuk belarusì. seryâ fìzìka-matèmatyčnyh navuk
Language(s) - English
Resource type - Journals
eISSN - 2524-2415
pISSN - 1561-2430
DOI - 10.29235/1561-2430-2021-57-2-176-184
Subject(s) - holomorphic function , mathematics , differentiable function , identity theorem , analyticity of holomorphic functions , uniqueness , pure mathematics , open mapping theorem (functional analysis) , function (biology) , norm (philosophy) , mathematical analysis , uniqueness theorem for poisson's equation , complex valued function , inverse function theorem , analytic function , picard–lindelöf theorem , fixed point theorem , lp space , banach space , banach manifold , evolutionary biology , political science , law , biology
In this article the relationship between the conditions of p-differentiability, p-holomorphycity, and the existence of the derivative of a function of a p-complex variable is considered. The general form of a p-holomorphic function is found. The sufficient conditions for p-analyticity and local invertibility are obtained. The open mapping theorem and the principle of maximum of the norm for a p-holomorphic function and the uniqueness theorem are proved.