A solution set analysis of a nonlinear operator equation using a Leray–Schauder type fixed point approach

Here we study the solution set of a nonlinear operator equation in a Banach subspace Ln⊂C(X)Ln⊂C(X) by reducing it to a Leray–Schauder type fixed point problem. The subspace LnLn is of finite codimension n∈Z+n∈Z+ in C(X)C(X), with XX an infinite compact Hausdorff space, and is defined by conditions αi∗(f)≔∫Xf(x)dμi(x)=0,f∈C(X), with norms ‖μi‖=1,i=1,…,n‖μi‖=1,i=1,…,n.