... complexBanach algebra satisfying each of the following:iA is self-adjoint,ii if f, g ∈ A such that |ϕ f |≤|ϕg| for each ϕ ∈ ΩA,then f ≤g,iii inf{r f : f ∈ A, f 1} > 0.Then ... function f in F such that f x/ f y;ii F is self-adjoint if f ∈Fimplies that f F; iii F is inverse-closed if 1 /f ∈Fwhenever f ∈Fand f x/ 0 for all x ∈ X.Let A be a unital commutative complex ... prove that for each n ∈ N the set {f m,0 ,f m,1, ,f m,n} is a linearly independent set of elements of Am. Therefore, Amis in nite dimensional.Hindawi Publishing CorporationFixed Point Theory...