### A general degree for function triples

#### Abstract

Consider a fixed class of maps $F$ for which there is a degree theory

for the coincidence problem $F(x)=\varphi(x)$ with compact $\varphi$.

It is proved that under very natural assumptions this degree extends

to a degree for function triples which in particular provides a degree

for coincidence inclusions $F(x)\in\Phi(x)$.

for the coincidence problem $F(x)=\varphi(x)$ with compact $\varphi$.

It is proved that under very natural assumptions this degree extends

to a degree for function triples which in particular provides a degree

for coincidence inclusions $F(x)\in\Phi(x)$.

#### Keywords

Fixed point index; degree theory; coincidence index; coincidence degree; multivalued map; nonlinear Fredholm map

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