IMPLICIT FUNCTION THEOREM IN SECTORIAL QUASI-NEIGHBORHOODS

Authors

  • R. Y. Leontyev Author

Abstract

We consider nonlinear operational equation $F(x,lambda)=0$ with condition $F(0,0)equiv0$. Operator $F_x(0,0)$ is not continuously inversible. We costruct continuous solutions $x(lambda)
ightarrow0$ as $lambda
ightarrow0$ in open set $S$ of linear normalized space $Lambda$. Zero belongs to frontier of set $S$. Solution existence theorems we have illustrated by examples.

Author Biography

  • R. Y. Leontyev
    Department of Mathematical Analysis

Issue

№ 15 (115), выпуск 1

Section

Mathematical Modelling