The aim of this paper is to solve the fixed point problems: <Equation ID="Equa"> <EquationSource Format="TEX">$$ v=\mathcal{O}v,\quad \hbox{with}\, \mathcal{O}v(x) \mathop{=}^{\rm def} \max (Lv(x), Bv(x) ), x \in \varepsilon, \quad (1)$$</EquationSource> </Equation> where <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$\varepsilon$$</EquationSource> </InlineEquation> is a finite set, L is contractive and B is a nonexpansive operator and <Equation ID="Equb"> <EquationSource Format="TEX">$$...</equationsource></equation></equationsource></inlineequation></equationsource></equation>

The aim of this paper is to solve the fixed point problems: $$ v=\mathcal{O}v,\quad \hbox{with}\, \mathcal{O}v(x) \mathop{=}^{\rm def} \max (Lv(x), Bv(x) ), x \in \varepsilon, \quad (1)$$ where $$\varepsilon$$ is a finite set, L is contractive and B is a nonexpansive operator and $$...