### A NEW SPECTRUM FOR NONLINEAR OPERATORS IN BANACH SPACES

#### Abstract

Given any continuous self-map f of a Banach space E over K (where K is R or C) and given any point p of E, we dene a subset (f, p) of K, called spectrum of f at p, which coincides with the usual spectrum (f) of f in the linear case. More generally, we show that (f, p) is always closed and, when f is C1, coincides with the spectrum (f′(p)) of the Frechet derivative of f at p. Some applications to bifurcation theory are given and some peculiar examples of spectra are provided.

### Refbacks

- There are currently no refbacks.

**ISSN: 1229-1595 (Print), 2466-0973 (Online)**

**(51767) 7 Kyungnamdaehak-ro, Masanhappo-gu, Changwon-si, Gyeongsangnam-do, Republic of Korea**